2.1 Problems not solved

Table 2.1: Problems not solved [1078]

#	ID	ODE	CAS classification	Maple solved?	Mma solved?
$1$	36	$$y^{\prime }=x^2-y^2$$ i.c.	[_Riccati]	✓	✓
$2$	529	$$y^{\prime }=x^2+y^2$$ i.c.	[[_Riccati, _special]]	✓	✓
$3$	1469	$$t{y}^{\prime \prime \prime }+2y^{\prime \prime }-y^{\prime }+ty=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$4$	1470	$$(2-t)y^{\prime \prime \prime }+(2t-3)y^{\prime \prime }-y^{\prime }t+y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$5$	1471	$$t^2(t+3)y^{\prime \prime \prime }-3t(t+2)y^{\prime \prime }+6(1+t)y^{\prime }-6y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$6$	1610	$$y^{\prime }=\tan \left(xy\right)$$	[‘y=_G(x,y’)‘]	✓	✓
$7$	1641	$$y^{\prime }-y=x\sqrt{y}$$ i.c. hint: bernoulli	[_Bernoulli]	✓	✓
$8$	1728	$$3x^2{y}^3-y^2+y+(-xy+2x)y^{\prime }=0$$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	✓
$9$	1753	$$(3x-1)y^{\prime \prime }-(3x+2)y^{\prime }+(6x-8)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$10$	1755	$$(2x+1)y^{\prime \prime }-2(2x^2-1)y^{\prime }-4(x+1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$11$	1823	$$\sin \left(x\right)y^{\prime \prime }+(2\sin \left(x\right)-\cos \left(x\right))y^{\prime }+(\sin \left(x\right)-\cos \left(x\right))y={\mathrm{e}}^{-x}$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$12$	2348	$$y^{\prime }=1+y+y^2\cos \left(t\right)$$ i.c.	[_Riccati]	✓	✗
$13$	2520	$$y^{\prime }=t^2+y^2$$ i.c.	[[_Riccati, _special]]	✓	✓
$14$	2523	$$y^{\prime }=1+y+y^2\cos \left(t\right)$$ i.c.	[_Riccati]	✓	✗
$15$	2945	$$(x-x\sqrt{x^2-y^2})y^{\prime }-y=0$$	[‘y=_G(x,y’)‘]	✓	✓
$16$	3003	$$(-x^2+1)y^{\prime }+xy=x(-x^2+1)\sqrt{y}$$ i.c. hint: bernoulli	[_rational, _Bernoulli]	✓	✓
$17$	3278	$$y{y}^{\prime \prime }=y^3+{y^{\prime }}^2$$ i.c.	[[_2nd_order, _missing_x]]	✓	✗
$18$	3279	$${(1+{y^{\prime }}^2)}^2=y^2{y}^{\prime \prime }$$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✗
$19$	3281	$$2y{y}^{\prime \prime }=y^3+2{y^{\prime }}^2$$ i.c.	[[_2nd_order, _missing_x]]	✓	✓
$20$	3492	$$-\frac{{y^{\prime }}^2}{y^2}+\frac{y^{\prime \prime }}{y}+\frac{2a\coth \left(2ax\right)y^{\prime }}{y}=2a^2$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$21$	3498	$$2y{y}^{\prime \prime \prime }+2(y+3y^{\prime })y^{\prime \prime }+2{y^{\prime }}^2=\sin \left(x\right)$$	[[_3rd_order, _exact, _nonlinear]]	✓	✓
$22$	4665	$$y^{\prime }=a{x}^{n-1}+b{x}^{2n}+c{y}^2$$	[_Riccati]	✓	✓
$23$	4685	$$y^{\prime }+(ax+y)y^2=0$$	[_Abel]	✓	✓
$24$	4686	$$y^{\prime }=(a{\mathrm{e}}^x+y)y^2$$	[_Abel]	✓	✓
$25$	4687	$$y^{\prime }+3a(2x+y)y^2=0$$	[_Abel]	✓	✓
$26$	4714	$$y^{\prime }+x(\sin \left(2y\right)-x^2\cos {\left(y\right)}^2)=0$$	[‘y=_G(x,y’)‘]	✓	✓
$27$	4722	$$y^{\prime }=\tan \left(x\right)(\tan \left(y\right)+\sec \left(x\right)\sec \left(y\right))$$	[‘y=_G(x,y’)‘]	✓	✓
$28$	4734	$$y^{\prime }=x^{m-1}{y}^{1-n}f(a{x}^m+b{y}^n)$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$29$	4796	$$y^{\prime }x=y+x\sqrt{x^2+y^2}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$30$	4797	$$y^{\prime }x=y-x(x-y)\sqrt{x^2+y^2}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$31$	4819	$$y^{\prime }x+ny=f\left(x\right)g\left(x^{n}y\right)$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$32$	4872	$$x^2{y}^{\prime }=a{x}^2{y}^2-a{y}^3$$	[_rational, _Abel]	✓	✓
$33$	4873	$$x^2{y}^{\prime }+a{y}^2+b{x}^2{y}^3=0$$	[_rational, _Abel]	✓	✓
$34$	4876	$$x^2{y}^{\prime }=\sec \left(y\right)+3x\tan \left(y\right)$$	[‘y=_G(x,y’)‘]	✓	✓
$35$	4898	$$(-x^2+1)y^{\prime }=n(1-2xy+y^2)$$	[_rational, _Riccati]	✓	✓
$36$	4901	$$(x^2+1)y^{\prime }=1+y^2-2xy(1+y^2)$$	[_rational, _Abel]	✓	✓
$37$	4902	$$(x^2+1)y^{\prime }+x\sin \left(y\right)\cos \left(y\right)=x(x^2+1)\cos {\left(y\right)}^2$$	[‘y=_G(x,y’)‘]	✓	✓
$38$	4942	$${(bx+a)}^2{y}^{\prime }+c{y}^2+(bx+a)y^3=0$$	[_rational, _Abel]	✓	✓
$39$	4952	$$x^3{y}^{\prime }=\cos \left(y\right)(\cos \left(y\right)-2x^2\sin \left(y\right))$$	[‘y=_G(x,y’)‘]	✓	✓
$40$	4980	$$x^7{y}^{\prime }+5x^3{y}^2+2(x^2+1)y^3=0$$	[_rational, _Abel]	✓	✓
$41$	4983	$$x^n{y}^{\prime }+x^{2n-2}+y^2+(1-n)x^{n-1}=0$$	[_Riccati]	✓	✗
$42$	5029	$$y{y}^{\prime }+x+f(x^2+y^2)g\left(x\right)=0$$	[NONE]	✓	✓
$43$	5089	$$(x+4x^3+5y)y^{\prime }+7x^3+3x^{2}y+4y=0$$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓
$44$	5160	$$(1-x^{2}y)y^{\prime }-1+x{y}^2=0$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$45$	5184	$$x^{7}y{y}^{\prime }=2x^2+2+5x^{3}y$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$46$	5204	$$(x+2y+y^2)y^{\prime }+y(1+y)+{(x+y)}^2{y}^2=0$$	[_rational]	✓	✓
$47$	5216	$$(\cot \left(x\right)-2y^2)y^{\prime }=y^3\csc \left(x\right)\sec \left(x\right)$$	[‘y=_G(x,y’)‘]	✓	✓
$48$	5273	$$(a-3x^2-y^2)y{y}^{\prime }+x(a-x^2+y^2)=0$$	[_rational]	✓	✓
$49$	5278	$$(x^2-x^3+3x{y}^2+2y^3)y^{\prime }+2x^3+3x^{2}y+y^2-y^3=0$$	[_rational]	✓	✓
$50$	5310	$$f\left(x\right)y^m{y}^{\prime }+g\left(x\right)y^{m+1}+h\left(x\right)y^n=0$$	[_Bernoulli]	✓	✓
$51$	5320	$$x(1-\sqrt{x^2-y^2})y^{\prime }=y$$	[‘y=_G(x,y’)‘]	✓	✓
$52$	5421	$$4{y^{\prime }}^2+2x{\mathrm{e}}^{-2y}{y}^{\prime }-{\mathrm{e}}^{-2y}=0$$	[[_1st_order, _with_linear_symmetries]]	✓	✓
$53$	5477	$$x^2{y^{\prime }}^2+2ax{y}^{\prime }+a^2+x^2-2ay=0$$	[_rational]	✓	✓
$54$	5479	$$x^2{y^{\prime }}^2-2x{y}^{\prime }y-x^4+(-x^2+1)y^2=0$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$55$	5500	$$(a^2-x^2){y^{\prime }}^2+2x{y}^{\prime }y+x^2=0$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$56$	5509	$$x(-x^2+1){y^{\prime }}^2-2(-x^2+1)y{y}^{\prime }+x(1-y^2)=0$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$57$	5551	$$y^2{y^{\prime }}^2-4ay{y}^{\prime }+4a^2-4ax+y^2=0$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$58$	5554	$$y^2{y^{\prime }}^2+2x{y}^{\prime }y+a-y^2=0$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$59$	5556	$$y^2{y^{\prime }}^2-2x{y}^{\prime }y+a-x^2+2y^2=0$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$60$	5557	$$y^2{y^{\prime }}^2+2axy{y}^{\prime }+(a-1)b+a{x}^2+(1-a)y^2=0$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$61$	5567	$$2y^2{y^{\prime }}^2+2x{y}^{\prime }y-1+x^2+y^2=0$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$62$	5574	$$(a-b)y^2{y^{\prime }}^2-2bxy{y}^{\prime }-ab-b{x}^2+a{y}^2=0$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$63$	5577	$$x{y}^2{y^{\prime }}^2+(a-x^3-y^3)y^{\prime }+x^{2}y=0$$	[_rational]	✓	✓
$64$	5583	$$9(-x^2+1)y^4{y^{\prime }}^2+6x{y}^5{y}^{\prime }+4x^2=0$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$65$	5605	$${y^{\prime }}^3+{\mathrm{e}}^{-2y}({\mathrm{e}}^{2x}+{\mathrm{e}}^{3x})y^{\prime }-{\mathrm{e}}^{3x-2y}=0$$	[‘y=_G(x,y’)‘]	✓	✗
$66$	5643	$$y^3{y^{\prime }}^3-(1-3x)y^2{y^{\prime }}^2+3x^{2}y{y}^{\prime }+x^3-y^2=0$$	[‘y=_G(x,y’)‘]	✓	✗
$67$	5688	$$\ln (\cos \left(y^{\prime }\right))+y^{\prime }\tan \left(y^{\prime }\right)=y$$ hint: dAlembert	[_dAlembert]	✓	✓
$68$	5767	$$y{y}^{\prime }=x+y^2-y^2{y^{\prime }}^2$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$69$	5884	$$(xy\sqrt{x^2-y^2}+x)y^{\prime }=y-x^2\sqrt{x^2-y^2}$$	[NONE]	✓	✓
$70$	6018	$$xy{y}^{\prime \prime }-2x{y^{\prime }}^2+(1+y)y^{\prime }=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$71$	6022	$$y^{\prime }-(y-f\left(x\right))(y-g\left(x\right))(y-\frac{af\left(x\right)+bg\left(x\right)}{a+b})h\left(x\right)-\frac{f^{\prime }\left(x\right)(y-g\left(x\right))}{f\left(x\right)-g\left(x\right)}-\frac{g^{\prime }\left(x\right)(y-f\left(x\right))}{g\left(x\right)-f\left(x\right)}=0$$	[_Abel]	✓	✓
$72$	6023	$$x^2{y}^{\prime }+x{y}^3+a{y}^2=0$$	[_rational, _Abel]	✓	✓
$73$	6024	$${(ax+b)}^2{y}^{\prime }+(ax+b)y^3+c{y}^2=0$$	[_rational, _Abel]	✓	✓
$74$	6316	$$y^{\prime }+y\sqrt{1+\sin {\left(x\right)}^2}=x$$ i.c.	[_linear]	✓	✓
$75$	6417	$$x{y}^{\prime \prime }+(1-x)y^{\prime }+my=0$$	[_Laguerre]	✓	✓
$76$	6604	$$x-2\sin \left(y\right)+3+(2x-4\sin \left(y\right)-3)\cos \left(y\right)y^{\prime }=0$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$77$	6652	$$(x-x\sqrt{x^2-y^2})y^{\prime }-y=0$$	[‘y=_G(x,y’)‘]	✓	✓
$78$	6662	$$4x^{2}y{y}^{\prime }=3x(3y^2+2)+2{(3y^2+2)}^3$$	[_rational]	✓	✓
$79$	6779	$$(2x-3)y^{\prime \prime \prime }-(6x-7)y^{\prime \prime }+4y^{\prime }x-4y=8$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$80$	6783	$$(1+2y+3y^2)y^{\prime \prime \prime }+6y^{\prime }(y^{\prime \prime }+{y^{\prime }}^2+3y{y}^{\prime \prime })=x$$	[[_3rd_order, _exact, _nonlinear]]	✓	✓
$81$	6784	$$3x(y^2{y}^{\prime \prime \prime }+6y{y}^{\prime }{y}^{\prime \prime }+2{y^{\prime }}^3)-3y(y{y}^{\prime \prime }+2{y^{\prime }}^2)=-\frac{2}{x}$$	[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]	✓	✓
$82$	6785	$$y{y}^{\prime \prime \prime }+3y^{\prime }{y}^{\prime \prime }-2y{y}^{\prime \prime }-2{y^{\prime }}^2+y{y}^{\prime }={\mathrm{e}}^{2x}$$	[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]	✓	✓
$83$	6816	$$x^3(x+1)y^{\prime \prime \prime }-(2+4x)x^2{y}^{\prime \prime }+(4+10x)x{y}^{\prime }-(4+12x)y=0$$ hint: series	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$84$	6817	$$x^3(x^2+1)y^{\prime \prime \prime }-(4x^2+2)x^2{y}^{\prime \prime }+(10x^2+4)x{y}^{\prime }-(12x^2+4)y=0$$ hint: series	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$85$	6876	$$(1-x)y^{\prime \prime }-4y^{\prime }x+5y=\cos \left(x\right)$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$86$	6978	$$y^{\prime }=x^2+y^2$$ i.c.	[[_Riccati, _special]]	✓	✓
$87$	7016	$$y^{\prime }=x^2-y^2$$ i.c.	[_Riccati]	✓	✓
$88$	7481	$$y^{\prime \prime }-\cot \left(x\right)y^{\prime }+\cos \left(x\right)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$89$	7496	$$x^2(x+1)y^{\prime \prime }+x(4x+3)y^{\prime }-y=x+\frac{1}{x}$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$90$	7500	$$(\cos \left(x\right)+\sin \left(x\right))y^{\prime \prime }-2\cos \left(x\right)y^{\prime }+(\cos \left(x\right)-\sin \left(x\right))y={(\cos \left(x\right)+\sin \left(x\right))}^2{\mathrm{e}}^{2x}$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$91$	7528	$$x^{2}y{y}^{\prime \prime }=x^2{y^{\prime }}^2-y^2$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$92$	7558	$$(-x^2+1)z^{\prime \prime }+(1-3x)z^{\prime }+kz=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$93$	7559	$$(-x^2+1){\eta }^{\prime \prime }-(x+1){\eta }^{\prime }+(k+1)\eta =0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$94$	7563	$$y^{\prime }x-y=x\sqrt{x^2-y^2}{y}^{\prime }$$	[‘y=_G(x,y’)‘]	✓	✓
$95$	7695	$$y^{\prime \prime \prime }-xy=0$$ i.c.	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$96$	7698	$$y^{\prime \prime }-2y^{\prime }x+2\alpha y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$97$	7766	$$y^{\prime \prime }=-\frac{1}{2{y^{\prime }}^2}$$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_poly_yn]]	✓	✓
$98$	7768	$$y^{\prime \prime }+\sin \left(y\right)=0$$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✗
$99$	7912	$$(x^2+2y^{\prime })y^{\prime \prime }+2y^{\prime }x=0$$ i.c.	[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]]	✓	✓
$100$	8014	$$y^{\prime \prime }-xf\left(x\right)y^{\prime }+f\left(x\right)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$101$	8160	$$x^3{y}^{\prime \prime \prime }+2x^2{y}^{\prime \prime }+(x^2+x)y^{\prime }+xy=0$$ hint: series	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$102$	8161	$$x^3{y}^{\prime \prime \prime }+x^2{y}^{\prime \prime }-3y^{\prime }x+(x-1)y=0$$ hint: series	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$103$	8162	$$x^3{y}^{\prime \prime \prime }-2x^2{y}^{\prime \prime }+(x^2+2x)y^{\prime }-xy=0$$ hint: series	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$104$	8163	$$x^3{y}^{\prime \prime \prime }+(2x^3-x^2)y^{\prime \prime }-y^{\prime }x+y=0$$ hint: series	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$105$	8764	$$y^{\prime \prime }+\frac{(t^2-1)y^{\prime }}{t}+\frac{t^{2}y}{{(1+{\mathrm{e}}^{\frac{t^2}{2}})}^2}=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$106$	8776	$$y^2{y}^{\prime \prime }=x$$	[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]	✓	✗
$107$	8803	$$y^{\prime \prime }-y{y}^{\prime }=2x$$	[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$108$	8815	$$y^{\prime \prime }-ax{y}^{\prime }-bxy-cx=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$109$	8816	$$y^{\prime \prime }-ax{y}^{\prime }-bxy-c{x}^2=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$110$	8817	$$y^{\prime \prime }-ax{y}^{\prime }-bxy-c{x}^3=0$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$111$	8846	$$y^{\prime \prime }-x^2{y}^{\prime }-x^{2}y-x^2=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$112$	8849	$$y^{\prime \prime }-x^2{y}^{\prime }-xy-x^2=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$113$	8850	$$y^{\prime \prime }-x^2{y}^{\prime }-x^{2}y-x^3-x^2=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$114$	8851	$$y^{\prime \prime }-x^2{y}^{\prime }-x^{3}y-x^4-x^2=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$115$	8852	$$y^{\prime \prime }-\frac{y^{\prime }}{x}-xy-x^2-\frac{1}{x}=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$116$	8854	$$y^{\prime \prime }-\frac{y^{\prime }}{x}-x^{3}y-x^4-\frac{1}{x}=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$117$	8856	$$y^{\prime \prime }-x^3{y}^{\prime }-x^{2}y-x^3=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$118$	8858	$$y^{\prime \prime \prime }-x^3{y}^{\prime }-x^{2}y-x^3=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$119$	8880	$$(x^2+1)y^{\prime \prime }+1+{y^{\prime }}^2=x$$	[[_2nd_order, _missing_y]]	✓	✗
$120$	8906	$$x{y}^{\prime \prime }+2y^{\prime }+xy=0$$ i.c. hint: series	[_Lienard]	✓	✓
$121$	8953	$$\frac{x{y}^{\prime \prime }}{1-x}+y=\frac{1}{1-x}$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$122$	8955	$$\frac{x{y}^{\prime \prime }}{1-x}+y=\cos \left(x\right)$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$123$	9005	$$c{y}^{\prime }=\frac{ax+b{y}^2}{rx}$$	[_rational, _Riccati]	✓	✓
$124$	9006	$$c{y}^{\prime }=\frac{ax+b{y}^2}{r{x}^2}$$	[_rational, _Riccati]	✓	✓
$125$	9074	$${y^{\prime \prime }}^n=0$$	[[_2nd_order, _quadrature]]	✓	✓
$126$	9126	$$y^{\prime \prime }+(1-x)y^{\prime }+y^2{y^{\prime }}^2=0$$	[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$127$	9127	$$y^{\prime \prime }+(\sin \left(x\right)+2x)y^{\prime }+\cos \left(y\right)y{y^{\prime }}^2=0$$	[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$128$	9131	$$y^{\prime \prime }+(3+x)y^{\prime }+(3+y^2){y^{\prime }}^2=0$$	[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$129$	9136	$$10y^{\prime \prime }+({\mathrm{e}}^x+3x)y^{\prime }+\frac{3{\mathrm{e}}^y{y^{\prime }}^2}{\sin \left(y\right)}=0$$	[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$130$	9144	$$(x^2+1)y^{\prime \prime }+(x+1)y^{\prime }+y=4\cos (\ln (x+1))$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✗
$131$	9159	$$x^2{y}^{\prime \prime }+{(y^{\prime }x-y)}^2=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$132$	9170	$$y^{\prime \prime \prime }-xy=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$133$	9238	$$(x^8+1)y^{\prime \prime }-16x^7{y}^{\prime }+72x^{6}y=0$$ hint: kovacic	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$134$	9658	$$(x^8+1)y^{\prime \prime }-16x^7{y}^{\prime }+72x^{6}y=0$$ hint: kovacic	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$135$	10047	$$y^{\prime }-\frac{y^2{f}^{\prime }\left(x\right)}{g\left(x\right)}+\frac{g^{\prime }\left(x\right)}{f\left(x\right)}=0$$	[_Riccati]	✓	✓
$136$	10050	$$y^{\prime }+y^3+ax{y}^2=0$$	[_Abel]	✓	✓
$137$	10051	$$y^{\prime }-y^3-a{\mathrm{e}}^x{y}^2=0$$	[_Abel]	✓	✓
$138$	10054	$$y^{\prime }+3a{y}^3+6ax{y}^2=0$$	[_Abel]	✓	✓
$139$	10056	$$y^{\prime }-x(x+2)y^3-(3+x)y^2=0$$	[_Abel]	✓	✓
$140$	10057	$$y^{\prime }+(4a^{2}x+3a{x}^2+b)y^3+3x{y}^2=0$$	[_Abel]	✓	✓
$141$	10059	$$y^{\prime }+2(a^2{x}^3-b^{2}x)y^3+3b{y}^2=0$$	[_Abel]	✓	✓
$142$	10064	$$y^{\prime }-(y-f\left(x\right))(y-g\left(x\right))(y-\frac{af\left(x\right)+bg\left(x\right)}{a+b})h\left(x\right)-\frac{f^{\prime }\left(x\right)(y-g\left(x\right))}{f\left(x\right)-g\left(x\right)}-\frac{g^{\prime }\left(x\right)(y-f\left(x\right))}{g\left(x\right)-f\left(x\right)}=0$$	[_Abel]	✓	✓
$143$	10066	$$y^{\prime }-f{\left(x\right)}^{1-n}{g}^{\prime }\left(x\right)y^n{(ag\left(x\right)+b)}^{-n}-\frac{f^{\prime }\left(x\right)y}{f\left(x\right)}-f\left(x\right)g^{\prime }\left(x\right)=0$$	[_Chini, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$144$	10067	$$y^{\prime }-a^{n}f{\left(x\right)}^{1-n}{g}^{\prime }\left(x\right)y^n-\frac{f^{\prime }\left(x\right)y}{f\left(x\right)}-f\left(x\right)g^{\prime }\left(x\right)=0$$	[_Chini, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$145$	10075	$$y^{\prime }-\frac{y-x^2\sqrt{x^2-y^2}}{xy\sqrt{x^2-y^2}+x}=0$$	[NONE]	✓	✓
$146$	10078	$$y^{\prime }-\sqrt{\frac{y^3+1}{x^3+1}}=0$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$147$	10093	$$y^{\prime }+f\left(x\right)\sin \left(y\right)+(1-f^{\prime }\left(x\right))\cos \left(y\right)-f^{\prime }\left(x\right)-1=0$$	[‘y=_G(x,y’)‘]	✓	✓
$148$	10094	$$y^{\prime }+2\tan \left(y\right)\tan \left(x\right)-1=0$$	[‘y=_G(x,y’)‘]	✓	✓
$149$	10096	$$y^{\prime }-\tan \left(xy\right)=0$$	[‘y=_G(x,y’)‘]	✓	✓
$150$	10098	$$y^{\prime }-x^{a-1}{y}^{1-b}f(\frac{x^a}{a}+\frac{y^b}{b})=0$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$151$	10100	$$2y^{\prime }-3y^2-4ay-b-c{\mathrm{e}}^{-2ax}=0$$	[_Riccati]	✓	✓
$152$	10123	$$y^{\prime }x+y^3+3x{y}^2=0$$	[_rational, _Abel]	✓	✓
$153$	10126	$$y^{\prime }x-x\sqrt{x^2+y^2}-y=0$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$154$	10127	$$y^{\prime }x-x(y-x)\sqrt{x^2+y^2}-y=0$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$155$	10131	$$y^{\prime }x-y(x\ln \left(\frac{x^2}{y}\right)+2)=0$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$156$	10139	$$y^{\prime }x+ay-f\left(x\right)g\left(x^{a}y\right)=0$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$157$	10156	$$x^2{y}^{\prime }+a{y}^3-a{x}^2{y}^2=0$$	[_rational, _Abel]	✓	✓
$158$	10157	$$x^2{y}^{\prime }+x{y}^3+a{y}^2=0$$	[_rational, _Abel]	✓	✓
$159$	10158	$$x^2{y}^{\prime }+a{x}^2{y}^3+b{y}^2=0$$	[_rational, _Abel]	✓	✓
$160$	10162	$$(x^2+1)y^{\prime }+(1+y^2)(2xy-1)=0$$	[_rational, _Abel]	✓	✓
$161$	10163	$$(x^2+1)y^{\prime }+x\sin \left(y\right)\cos \left(y\right)-x(x^2+1)\cos {\left(y\right)}^2=0$$	[‘y=_G(x,y’)‘]	✓	✓
$162$	10168	$$(x^2-1)y^{\prime }+a(1-2xy+y^2)=0$$	[_rational, _Riccati]	✓	✓
$163$	10180	$${(ax+b)}^2{y}^{\prime }+(ax+b)y^3+c{y}^2=0$$	[_rational, _Abel]	✓	✓
$164$	10196	$$x^7{y}^{\prime }+5x^3{y}^2+2(x^2+1)y^3=0$$	[_rational, _Abel]	✓	✓
$165$	10222	$$y{y}^{\prime }+x+f(x^2+y^2)g\left(x\right)=0$$	[NONE]	✓	✓
$166$	10261	$$(x^{2}y-1)y^{\prime }-x{y}^2+1=0$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$167$	10266	$$x(xy+x^4-1)y^{\prime }-y(xy-x^4-1)=0$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$168$	10275	$$(y-x)\sqrt{x^2+1}{y}^{\prime }-a\sqrt{{(1+y^2)}^3}=0$$	[‘x=_G(y,y’)‘]	✓	✓
$169$	10287	$$(x+2y+y^2)y^{\prime }+y(1+y)+{(x+y)}^2{y}^2=0$$	[_rational]	✓	✓
$170$	10320	$$(\frac{y^2}{b}+\frac{x^2}{a})(y{y}^{\prime }+x)+\frac{(a-b)(y{y}^{\prime }-x)}{a+b}=0$$	[_rational]	✓	✓
$171$	10321	$$(2a{y}^3+3ax{y}^2-b{x}^3+c{x}^2)y^{\prime }-a{y}^3+c{y}^2+3b{x}^{2}y+2b{x}^3=0$$	[_rational]	✓	✓
$172$	10357	$$y^{\prime }\cos \left(y\right)-\cos \left(x\right)\sin {\left(y\right)}^2-\sin \left(y\right)=0$$	[‘y=_G(x,y’)‘]	✓	✓
$173$	10358	$$y^{\prime }\cos \left(y\right)+x\sin \left(y\right)\cos {\left(y\right)}^2-\sin {\left(y\right)}^3=0$$	[‘y=_G(x,y’)‘]	✓	✓
$174$	10364	$$x{y}^{\prime }\ln \left(x\right)\sin \left(y\right)+\cos \left(y\right)(1-x\cos \left(y\right))=0$$	[‘y=_G(x,y’)‘]	✓	✓
$175$	10373	$$f(x^2+a{y}^2)(ay{y}^{\prime }+x)-y-y^{\prime }x=0$$	[_exact]	✓	✓
$176$	10435	$${(y^{\prime }x+a)}^2-2ay+x^2=0$$	[_rational]	✓	✓
$177$	10439	$$x^2{y^{\prime }}^2-2x{y}^{\prime }y-x^4+(-x^2+1)y^2=0$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$178$	10452	$$(-a^2+x^2){y^{\prime }}^2-2x{y}^{\prime }y-x^2=0$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$179$	10458	$$x(x^2-1){y^{\prime }}^2+2(-x^2+1)y{y}^{\prime }+x{y}^2-x=0$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$180$	10461	$${\mathrm{e}}^{-2x}{y^{\prime }}^2-{(y^{\prime }-1)}^2+{\mathrm{e}}^{-2y}=0$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$181$	10489	$$y^2{y^{\prime }}^2-4ay{y}^{\prime }+4a^2-4ax+y^2=0$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$182$	10490	$$y^2{y^{\prime }}^2+2x{y}^{\prime }y+a{y}^2+bx+c=0$$	[_rational]	✓	✓
$183$	10491	$$y^2{y^{\prime }}^2-2x{y}^{\prime }y+a-x^2+2y^2=0$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$184$	10492	$$y^2{y^{\prime }}^2+2axy{y}^{\prime }+(a-1)b+a{x}^2+(1-a)y^2=0$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$185$	10494	$$(y^2-2ax+a^2){y^{\prime }}^2+2ay{y}^{\prime }+y^2=0$$	[‘y=_G(x,y’)‘]	✓	✓
$186$	10501	$$(a-b)y^2{y^{\prime }}^2-2bxy{y}^{\prime }-ab-b{x}^2+a{y}^2=0$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$187$	10502	$$(a{y}^2+bx+c){y^{\prime }}^2-by{y}^{\prime }+d{y}^2=0$$	[‘y=_G(x,y’)‘]	✓	✓
$188$	10505	$$x{y}^2{y^{\prime }}^2-(y^3+x^3-a)y^{\prime }+x^{2}y=0$$	[_rational]	✓	✓
$189$	10508	$$(y^4-a^2{x}^2){y^{\prime }}^2+2a^{2}xy{y}^{\prime }+y^2(y^2-a^2)=0$$	[‘y=_G(x,y’)‘]	✓	✓
$190$	10509	$$(y^4+x^2{y}^2-x^2){y^{\prime }}^2+2x{y}^{\prime }y-y^2=0$$	[‘y=_G(x,y’)‘]	✓	✓
$191$	10510	$$9y^4(x^2-1){y^{\prime }}^2-6x{y}^5{y}^{\prime }-4x^2=0$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$192$	10512	$$(a^2\sqrt{x^2+y^2}-x^2){y^{\prime }}^2+2x{y}^{\prime }y+a^2\sqrt{x^2+y^2}-y^2=0$$	[[_1st_order, _with_linear_symmetries]]	✓	✓
$193$	10513	$$(a{(x^2+y^2)}^{3/2}-x^2){y^{\prime }}^2+2x{y}^{\prime }y+a{(x^2+y^2)}^{3/2}-y^2=0$$	[[_1st_order, _with_linear_symmetries]]	✓	✓
$194$	10516	$$f(x^2+y^2)(1+{y^{\prime }}^2)-{(y^{\prime }x-y)}^2=0$$	[[_1st_order, _with_linear_symmetries]]	✓	✓
$195$	10562	$$f(x^2+y^2)\sqrt{1+{y^{\prime }}^2}-y^{\prime }x+y=0$$	[[_1st_order, _with_linear_symmetries]]	✓	✓
$196$	10579	$$y^{\prime }=\frac{1+2F\left(\frac{4x^{2}y+1}{4x^2}\right)x}{2x^3}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$197$	10580	$$y^{\prime }=\frac{1+F\left(\frac{yax+1}{ax}\right)a{x}^2}{a{x}^2}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$198$	10581	$$y^{\prime }=-\frac{(a{x}^2-2F(y+\frac{a{x}^4}{8}))x}{2}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$199$	10583	$$y^{\prime }=F(\ln (\ln \left(y\right))-\ln \left(x\right))y$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$200$	10584	$$y^{\prime }=\frac{F\left(\frac{y}{\sqrt{x^2+1}}\right)x}{\sqrt{x^2+1}}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$201$	10585	$$y^{\prime }=\frac{(x^{3/2}+2F(y-\frac{x^3}{6}))\sqrt{x}}{2}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$202$	10586	$$y^{\prime }=\frac{x+F(-(x-y)(x+y))}{y}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$203$	10588	$$y^{\prime }=\frac{x}{-y+F(x^2+y^2)}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$204$	10589	$$y^{\prime }=\frac{F\left(\frac{a{y}^2+b{x}^2}{a}\right)x}{\sqrt{a}y}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$205$	10590	$$y^{\prime }=\frac{6x^3+5\sqrt{x}+5F(y-\frac{2x^3}{5}-2\sqrt{x})}{5x}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$206$	10591	$$y^{\prime }=\frac{F(y^{3/2}-\frac{3{\mathrm{e}}^x}{2}){\mathrm{e}}^x}{\sqrt{y}}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$207$	10592	$$y^{\prime }=\frac{F(-\frac{-y^2+b}{x^2})x}{y}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$208$	10593	$$y^{\prime }=\frac{F\left(\frac{x{y}^2+1}{x}\right)}{y{x}^2}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$209$	10597	$$y^{\prime }=\frac{-x+F(x^2+y^2)}{y}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$210$	10599	$$y^{\prime }=\frac{F(-(x-y)(x+y))x}{y}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$211$	10600	$$y^{\prime }=\frac{y^2(2+F\left(\frac{x^2-y}{y{x}^2}\right)x^2)}{x^3}$$	[NONE]	✓	✓
$212$	10601	$$y^{\prime }=\frac{2F(y+\ln (2x+1))x+F(y+\ln (2x+1))-2}{2x+1}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$213$	10602	$$y^{\prime }=\frac{2y^3}{1+2F\left(\frac{1+4x{y}^2}{y^2}\right)y}$$	[‘x=_G(y,y’)‘]	✓	✓
$214$	10604	$$y^{\prime }=-(-{\mathrm{e}}^{-x^2}+x^2{\mathrm{e}}^{-x^2}-F(y-\frac{x^2{\mathrm{e}}^{-x^2}}{2}))x$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$215$	10605	$$y^{\prime }=\frac{2y+F\left(\frac{y}{x^2}\right)x^3}{x}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$216$	10607	$$y^{\prime }=\frac{-3x^{2}y+F\left(x^{3}y\right)}{x^3}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$217$	10609	$$y^{\prime }=\frac{-2x-y+F\left((x+y)x\right)}{x}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$218$	10611	$$y^{\prime }=\frac{x+y+F(-\frac{-y+x\ln \left(x\right)}{x})x^2}{x}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$219$	10612	$$y^{\prime }=\frac{x(a-1)(a+1)}{y+F(\frac{y^2}{2}-\frac{a^2{x}^2}{2}+\frac{x^2}{2})a^2-F(\frac{y^2}{2}-\frac{a^2{x}^2}{2}+\frac{x^2}{2})}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$220$	10613	$$y^{\prime }=\frac{y}{x(-1+F\left(xy\right)y)}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$221$	10615	$$y^{\prime }=\frac{F\left(\frac{(3+y){\mathrm{e}}^{\frac{3x^2}{2}}}{3y}\right)x{y}^2{\mathrm{e}}^{3x^2}{\mathrm{e}}^{-\frac{9x^2}{2}}}{9}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$222$	10616	$$y^{\prime }=\frac{(1+y)((y-\ln (1+y)-\ln \left(x\right))x+1)}{yx}$$	[‘y=_G(x,y’)‘]	✓	✓
$223$	10617	$$y^{\prime }=\frac{6y}{8y^4+9y^3+12y^2+6y-F(-\frac{y^4}{3}-\frac{y^3}{2}-y^2-y+x)}$$	[‘x=_G(y,y’)‘]	✓	✓
$224$	10623	$$y^{\prime }=\frac{i{x}^2(i-2\sqrt{-x^3+6y})}{2}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$225$	10624	$$y^{\prime }=\frac{x}{y+\sqrt{x^2+1}}$$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	✓
$226$	10632	$$y^{\prime }=\frac{1+2x^5\sqrt{4x^{2}y+1}}{2x^3}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$227$	10635	$$y^{\prime }=\frac{{\mathrm{e}}^{-x^2}x}{y{\mathrm{e}}^{x^2}+1}$$	[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$228$	10636	$$y^{\prime }=-(-\ln (\ln \left(y\right))+\ln \left(x\right))y$$	[‘x=_G(y,y’)‘]	✓	✓
$229$	10637	$$y^{\prime }={(-\ln (\ln \left(y\right))+\ln \left(x\right))}^{2}y$$	[‘y=_G(x,y’)‘]	✓	✓
$230$	10638	$$y^{\prime }=\frac{y}{\ln (\ln \left(y\right))-\ln \left(x\right)+1}$$	[‘y=_G(x,y’)‘]	✓	✓
$231$	10639	$$y^{\prime }=\frac{1+2\sqrt{4x^{2}y+1}{x}^4}{2x^3}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$232$	10640	$$y^{\prime }=\frac{{(-y^2+4ax)}^2}{y}$$	[_rational]	✓	✓
$233$	10642	$$y^{\prime }=-\frac{x^2(ax-2\sqrt{a(a{x}^4+8y)})}{2}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$234$	10645	$$y^{\prime }=\frac{{(a{y}^2+b{x}^2)}^{2}x}{a^{5/2}y}$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$235$	10646	$$y^{\prime }=-\frac{x^3(\sqrt{a}x+\sqrt{a}-2\sqrt{a{x}^4+8y})\sqrt{a}}{2(x+1)}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$236$	10650	$$y^{\prime }=\frac{2a+x\sqrt{-y^2+4ax}}{y}$$	[‘y=_G(x,y’)‘]	✓	✓
$237$	10661	$$y^{\prime }=\frac{2a+x^2\sqrt{-y^2+4ax}}{y}$$	[‘y=_G(x,y’)‘]	✓	✓
$238$	10663	$$y^{\prime }=-\frac{(\sqrt{a}{x}^4+\sqrt{a}{x}^3-2\sqrt{a{x}^4+8y})\sqrt{a}}{2(x+1)}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$239$	10667	$$y^{\prime }=\frac{{(-2y^{3/2}+3{\mathrm{e}}^x)}^2{\mathrm{e}}^x}{4\sqrt{y}}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$240$	10668	$$y^{\prime }=\frac{ix(i-2\sqrt{-x^2+4\ln \left(a\right)+4\ln \left(y\right)})y}{2}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$241$	10669	$$y^{\prime }=\frac{{(x{y}^2+1)}^2}{y{x}^4}$$	[_rational]	✓	✓
$242$	10670	$$y^{\prime }=\frac{x^2(3x+\sqrt{-9x^4+4y^3})}{y^2}$$	[‘y=_G(x,y’)‘]	✓	✓
$243$	10674	$$y^{\prime }=\frac{x+1+2x^6\sqrt{4x^{2}y+1}}{2x^3(x+1)}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$244$	10676	$$y^{\prime }=\frac{x^2(x+1+2x\sqrt{x^3-6y})}{2x+2}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$245$	10682	$$y^{\prime }=\frac{y+\sqrt{x^2+y^2}{x}^2}{x}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$246$	10684	$$y^{\prime }=\frac{y^{3}x{\mathrm{e}}^{2x^2}}{y{\mathrm{e}}^{x^2}+1}$$	[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$247$	10688	$$y^{\prime }=\frac{-x^2+1+4x^3\sqrt{x^2-2x+1+8y}}{4x+4}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$248$	10690	$$y^{\prime }=\frac{y+x^3\sqrt{x^2+y^2}}{x}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$249$	10692	$$y^{\prime }=\frac{x+1+2\sqrt{4x^{2}y+1}{x}^3}{2x^3(x+1)}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$250$	10697	$$y^{\prime }=\frac{x(-2x-2+3x^2\sqrt{x^2+3y})}{3x+3}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$251$	10699	$$y^{\prime }=\frac{2x{\mathrm{e}}^x-2x-\ln \left(x\right)-1+x^4\ln \left(x\right)+x^4-2y{x}^2\ln \left(x\right)-2x^{2}y+y^2\ln \left(x\right)+y^2}{{\mathrm{e}}^x-1}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	✓
$252$	10704	$$y^{\prime }=-\frac{(-\ln (-1+y)+\ln (1+y)+2\ln \left(x\right))x{(1+y)}^2}{8}$$	[‘y=_G(x,y’)‘]	✓	✓
$253$	10705	$$y^{\prime }=\frac{{(-\ln (-1+y)+\ln (1+y)+2\ln \left(x\right))}^{2}x{(1+y)}^2}{16}$$	[‘y=_G(x,y’)‘]	✓	✓
$254$	10706	$$y^{\prime }=\frac{{(-y^2+4ax)}^3}{(-y^2+4ax-1)y}$$	[_rational]	✓	✓
$255$	10707	$$y^{\prime }=\frac{2ax+2a+x^3\sqrt{-y^2+4ax}}{(x+1)y}$$	[‘y=_G(x,y’)‘]	✓	✓
$256$	10709	$$y^{\prime }=-\frac{(\ln \left(y\right)x+\ln \left(y\right)-1)y}{x+1}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$257$	10710	$$y^{\prime }=\frac{x^2+2x+1+2x^3\sqrt{x^2+2x+1-4y}}{2x+2}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$258$	10713	$$y^{\prime }=\frac{-x^2+x+2+2x^3\sqrt{x^2-4x+4y}}{2x+2}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$259$	10714	$$y^{\prime }=\frac{3x^4+3x^3+\sqrt{9x^4-4y^3}}{(x+1)y^2}$$	[_rational]	✓	✓
$260$	10718	$$y^{\prime }=\frac{x^3(3x+3+\sqrt{9x^4-4y^3})}{(x+1)y^2}$$	[‘y=_G(x,y’)‘]	✓	✓
$261$	10725	$$y^{\prime }=\frac{(2x+2+y)y}{(\ln \left(y\right)+2x-1)(x+1)}$$	[‘x=_G(y,y’)‘]	✓	✓
$262$	10728	$$y^{\prime }=\frac{{(2y^{3/2}-3{\mathrm{e}}^x)}^3{\mathrm{e}}^x}{4(2y^{3/2}-3{\mathrm{e}}^x+2)\sqrt{y}}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$263$	10730	$$y^{\prime }=\frac{-x^2-x-ax-a+2x^3\sqrt{x^2+2ax+a^2+4y}}{2x+2}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$264$	10731	$$y^{\prime }=\frac{2x\sin \left(x\right)-\ln \left(2x\right)+\ln \left(2x\right)x^4-2\ln \left(2x\right)x^{2}y+\ln \left(2x\right)y^2}{\sin \left(x\right)}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	✓
$265$	10732	$$y^{\prime }=\frac{(-\ln \left(y\right)x-\ln \left(y\right)+x^3)y}{x+1}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$266$	10735	$$y^{\prime }=\frac{x(-1+x-2xy+2x^3)}{x^2-y}$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓
$267$	10738	$$y^{\prime }=\frac{x+y^4-2x^2{y}^2+x^4}{y}$$	[_rational]	✓	✓
$268$	10739	$$y^{\prime }=\frac{{(a{y}^2+b{x}^2)}^{3}x}{a^{5/2}(a{y}^2+b{x}^2+a)y}$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$269$	10740	$$y^{\prime }=-\frac{\cos \left(y\right)(x-\cos \left(y\right)+1)}{(x\sin \left(y\right)-1)(x+1)}$$	[‘y=_G(x,y’)‘]	✓	✓
$270$	10741	$$y^{\prime }=-\frac{i(8ix+16y^4+8x^2{y}^2+x^4)}{32y}$$	[_rational]	✓	✓
$271$	10742	$$y^{\prime }=\frac{x}{-y+x^4+2x^2{y}^2+y^4}$$	[_rational]	✓	✓
$272$	10744	$$y^{\prime }=-\frac{i(ix+x^4+2x^2{y}^2+y^4)}{y}$$	[_rational]	✓	✓
$273$	10747	$$y^{\prime }=\frac{{(x-y)}^2{(x+y)}^{2}x}{y}$$	[_rational]	✓	✓
$274$	10750	$$y^{\prime }=\frac{\cos \left(y\right)(\cos \left(y\right)x^3-x-1)}{(x\sin \left(y\right)-1)(x+1)}$$	[‘y=_G(x,y’)‘]	✓	✓
$275$	10751	$$y^{\prime }=\frac{(x+1+x^4\ln \left(y\right))y\ln \left(y\right)}{x(x+1)}$$	[‘x=_G(y,y’)‘]	✓	✓
$276$	10754	$$y^{\prime }=\frac{2x^{3}y+x^6+x^2{y}^2+y^3}{x^4}$$	[_rational, _Abel]	✓	✓
$277$	10756	$$y^{\prime }=\frac{(2x+2+x^{3}y)y}{(\ln \left(y\right)+2x-1)(x+1)}$$	[‘x=_G(y,y’)‘]	✓	✓
$278$	10757	$$y^{\prime }=-\frac{i(54i{x}^2+81y^4+18x^4{y}^2+x^8)x}{243y}$$	[_rational]	✓	✓
$279$	10758	$$y^{\prime }=\frac{{(x{y}^2+1)}^3}{x^4(x{y}^2+1+x)y}$$	[_rational]	✓	✓
$280$	10760	$$y^{\prime }=-\frac{(\ln \left(y\right)x+\ln \left(y\right)-x)y}{x(x+1)}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$281$	10762	$$y^{\prime }=\frac{(-\ln \left(y\right)x-\ln \left(y\right)+x^4)y}{x(x+1)}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$282$	10767	$$y^{\prime }=-\frac{i(16i{x}^2+16y^4+8x^4{y}^2+x^8)x}{32y}$$	[_rational]	✓	✓
$283$	10770	$$y^{\prime }=\frac{(x+1+\ln \left(y\right)x)\ln \left(y\right)y}{x(x+1)}$$	[‘x=_G(y,y’)‘]	✓	✓
$284$	10776	$$y^{\prime }=\frac{-3x^{2}y+1+y^2{x}^6+y^3{x}^9}{x^3}$$	[_rational, _Abel]	✓	✓
$285$	10778	$$y^{\prime }=\frac{xy+y+x\sqrt{x^2+y^2}}{x(x+1)}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$286$	10785	$$y^{\prime }=\frac{x(-x-1+x^2-2x^{2}y+2x^4)}{(x^2-y)(x+1)}$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$287$	10789	$$y^{\prime }=\frac{2x^2\cosh \left(\frac{1}{x-1}\right)-2x\cosh \left(\frac{1}{x-1}\right)-1+y^2-2x^{2}y+x^4-x+x{y}^2-2x^{3}y+x^5}{(x-1)\cosh \left(\frac{1}{x-1}\right)}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	✓
$288$	10792	$$y^{\prime }=\frac{y}{x(-1+y+x^2{y}^3+y^4{x}^3)}$$	[_rational]	✓	✓
$289$	10794	$$y^{\prime }=\frac{y^{3}x{\mathrm{e}}^{3x^2}{\mathrm{e}}^{-\frac{9x^2}{2}}}{9{\mathrm{e}}^{\frac{3x^2}{2}}+3{\mathrm{e}}^{\frac{3x^2}{2}}y+9y}$$	[[_Abel, ‘2nd type‘, ‘class C‘]]	✓	✓
$290$	10796	$$y^{\prime }=\frac{(x+y+1)y}{(2y^3+y+x)(x+1)}$$	[_rational]	✓	✓
$291$	10800	$$y^{\prime }=-\frac{-\frac{1}{x}-\mathit{\text{\_F1}}(y+\frac{1}{x})}{x}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$292$	10801	$$y^{\prime }=\frac{\mathit{\text{\_F1}}(y^2-2\ln \left(x\right))}{\sqrt{y^2}x}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$293$	10802	$$y^{\prime }=\frac{-\sin \left(2y\right)x-\sin \left(2y\right)+\cos \left(2y\right)x^4+x^4}{2x(x+1)}$$	[‘y=_G(x,y’)‘]	✓	✓
$294$	10803	$$y^{\prime }=\frac{xy+y+x^4\sqrt{x^2+y^2}}{x(x+1)}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$295$	10804	$$y^{\prime }=\frac{-\sin \left(2y\right)x-\sin \left(2y\right)+x\cos \left(2y\right)+x}{2x(x+1)}$$	[‘y=_G(x,y’)‘]	✓	✓
$296$	10805	$$y^{\prime }=-\frac{1}{-x-\mathit{\text{\_F1}}(y-\ln \left(x\right))y{\mathrm{e}}^y}$$	[NONE]	✓	✓
$297$	10809	$$y^{\prime }=\frac{x^3{\mathrm{e}}^y+x^4+{\mathrm{e}}^{y}y-{\mathrm{e}}^y\ln ({\mathrm{e}}^y+x)+xy-\ln ({\mathrm{e}}^y+x)x+x}{x^2}$$	[‘y=_G(x,y’)‘]	✓	✓
$298$	10810	$$y^{\prime }=\frac{x^2}{2}+\sqrt{x^3-6y}+x^2\sqrt{x^3-6y}+x^3\sqrt{x^3-6y}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$299$	10811	$$y^{\prime }=\frac{(-\sqrt{a}{x}^3+2\sqrt{a{x}^4+8y}+2x^2\sqrt{a{x}^4+8y}+2x^3\sqrt{a{x}^4+8y})\sqrt{a}}{2}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$300$	10812	$$y^{\prime }=\frac{y(-3x^{3}y-3+y^2{x}^7)}{x(x^{3}y+1)}$$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$301$	10813	$$y^{\prime }=\frac{{(3+y)}^3{\mathrm{e}}^{\frac{9x^2}{2}}x{\mathrm{e}}^{\frac{3x^2}{2}}{\mathrm{e}}^{-3x^2}}{243{\mathrm{e}}^{\frac{3x^2}{2}}+81{\mathrm{e}}^{\frac{3x^2}{2}}y+243y}$$	[[_Abel, ‘2nd type‘, ‘class C‘]]	✓	✓
$302$	10814	$$y^{\prime }=\frac{{(x-y)}^3{(x+y)}^{3}x}{(-y^2+x^2-1)y}$$	[_rational]	✓	✓
$303$	10815	$$y^{\prime }=\frac{-2\cos \left(y\right)+x^3\cos \left(2y\right)\ln \left(x\right)+x^3\ln \left(x\right)}{2\sin \left(y\right)\ln \left(x\right)x}$$	[‘y=_G(x,y’)‘]	✓	✓
$304$	10817	$$y^{\prime }=-\frac{2x}{3}+\sqrt{x^2+3y}+x^2\sqrt{x^2+3y}+x^3\sqrt{x^2+3y}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$305$	10818	$$y^{\prime }=\frac{-2\cos \left(y\right)+x^2\cos \left(2y\right)\ln \left(x\right)+x^2\ln \left(x\right)}{2\sin \left(y\right)\ln \left(x\right)x}$$	[‘y=_G(x,y’)‘]	✓	✓
$306$	10823	$$y^{\prime }=\frac{({(x^2+1)}^{3/2}{x}^2+{(x^2+1)}^{3/2}+y^2{(x^2+1)}^{3/2}+x^2{y}^3+y^3)x}{{(x^2+1)}^3}$$	[_Abel]	✓	✓
$307$	10824	$$y^{\prime }=\frac{(3x{y}^2+x+3y^2)y}{(6y^2+x)x(x+1)}$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$308$	10825	$$y^{\prime }=-\frac{-y+x^3\sqrt{x^2+y^2}-x^2\sqrt{x^2+y^2}y}{x}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$309$	10827	$$y^{\prime }=\frac{1+2\sqrt{4x^{2}y+1}{x}^3+2x^5\sqrt{4x^{2}y+1}+2x^6\sqrt{4x^{2}y+1}}{2x^3}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$310$	10829	$$y^{\prime }=\frac{2a+\sqrt{-y^2+4ax}+x^2\sqrt{-y^2+4ax}+x^3\sqrt{-y^2+4ax}}{y}$$	[‘y=_G(x,y’)‘]	✓	✓
$311$	10830	$$y^{\prime }=\frac{(x+y+1)y}{(y^4+y^3+y^2+x)(x+1)}$$	[_rational]	✓	✓
$312$	10831	$$y^{\prime }=-\frac{-y+x^4\sqrt{x^2+y^2}-x^3\sqrt{x^2+y^2}y}{x}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$313$	10832	$$y^{\prime }=\frac{(x^4+3x{y}^2+3y^2)y}{(6y^2+x)x(x+1)}$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$314$	10838	$$y^{\prime }=\frac{b{x}^3+c^2\sqrt{a}-2cb{x}^2\sqrt{a}+2c{y}^2{a}^{3/2}+b^2{x}^4\sqrt{a}-2y^2{a}^{3/2}b{x}^2+a^{5/2}{y}^4}{a{x}^{2}y}$$	[_rational]	✓	✓
$315$	10842	$$y^{\prime }=\frac{3x^3+\sqrt{-9x^4+4y^3}+x^2\sqrt{-9x^4+4y^3}+x^3\sqrt{-9x^4+4y^3}}{y^2}$$	[NONE]	✓	✓
$316$	10843	$$y^{\prime }=\frac{1}{-x+(\frac{1}{y}+1)x+\mathit{\text{\_F1}}\left((\frac{1}{y}+1)x\right)x^2-\mathit{\text{\_F1}}\left((\frac{1}{y}+1)x\right)x^2(\frac{1}{y}+1)}$$	[‘y=_G(x,y’)‘]	✓	✓
$317$	10844	$$y^{\prime }=\frac{x}{2}+\frac{1}{2}+\sqrt{x^2+2x+1-4y}+x^2\sqrt{x^2+2x+1-4y}+x^3\sqrt{x^2+2x+1-4y}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$318$	10845	$$y^{\prime }=\frac{\cosh \left(x\right)}{\sinh \left(x\right)}+\mathit{\text{\_F1}}(y-\ln (\sinh \left(x\right)))$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$319$	10846	$$y^{\prime }=-\frac{x}{2}+1+\sqrt{x^2-4x+4y}+x^2\sqrt{x^2-4x+4y}+x^3\sqrt{x^2-4x+4y}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$320$	10847	$$y^{\prime }=\frac{1}{\sin \left(x\right)}+\mathit{\text{\_F1}}(y-\ln (\sin \left(x\right))+\ln (\cos \left(x\right)+1))$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$321$	10851	$$y^{\prime }=\frac{y(\ln \left(x\right)+\ln \left(y\right)-1+x^2\ln {\left(x\right)}^2+2x^2\ln \left(y\right)\ln \left(x\right)+x^2\ln {\left(y\right)}^2)}{x}$$	[NONE]	✓	✓
$322$	10852	$$y^{\prime }=\frac{y(\ln \left(y\right)-1+\ln \left(x\right)+x^3\ln {\left(x\right)}^2+2x^3\ln \left(y\right)\ln \left(x\right)+x^3\ln {\left(y\right)}^2)}{x}$$	[NONE]	✓	✓
$323$	10853	$$y^{\prime }=-\frac{(-\frac{1}{x}-\mathit{\text{\_F1}}(y^2-2x))x}{\sqrt{y^2}}$$	[NONE]	✓	✓
$324$	10854	$$y^{\prime }=-\frac{x}{4}+\frac{1}{4}+\sqrt{x^2-2x+1+8y}+x^2\sqrt{x^2-2x+1+8y}+x^3\sqrt{x^2-2x+1+8y}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$325$	10856	$$y^{\prime }=-\frac{-x-\mathit{\text{\_F1}}(y^2-2x)}{\sqrt{y^2}x}$$	[NONE]	✓	✓
$326$	10858	$$y^{\prime }=-\frac{(-\frac{y{\mathrm{e}}^{\frac{1}{x}}}{x}-\mathit{\text{\_F1}}\left(y{\mathrm{e}}^{\frac{1}{x}}\right)){\mathrm{e}}^{-\frac{1}{x}}}{x}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$327$	10859	$$y^{\prime }=\frac{y+x\sqrt{x^2+y^2}+x^3\sqrt{x^2+y^2}+x^4\sqrt{x^2+y^2}}{x}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$328$	10861	$$y^{\prime }=(\frac{\ln (-1+y)y}{(1-y)\ln \left(x\right)x}-\frac{\ln (-1+y)}{(1-y)\ln \left(x\right)x}-f\left(x\right))(1-y)$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$329$	10862	$$y^{\prime }=-\frac{x}{2}-\frac{a}{2}+\sqrt{x^2+2ax+a^2+4y}+x^2\sqrt{x^2+2ax+a^2+4y}+x^3\sqrt{x^2+2ax+a^2+4y}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$330$	10865	$$y^{\prime }=\frac{-x+1-2y+3x^2-2x^{2}y+2x^4+x^3-2x^{3}y+2x^5}{x^2-y}$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓
$331$	10866	$$y^{\prime }=\frac{({\mathrm{e}}^{-\frac{y}{x}}y+{\mathrm{e}}^{-\frac{y}{x}}x+x+x^3+x^4){\mathrm{e}}^{\frac{y}{x}}}{x}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$332$	10871	$$y^{\prime }=-\frac{-xy-y+x^5\sqrt{x^2+y^2}-x^4\sqrt{x^2+y^2}y}{x(x+1)}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$333$	10874	$$y^{\prime }=\frac{1+y^4-8ax{y}^2+16a^2{x}^2+y^6-12y^{4}ax+48y^2{a}^2{x}^2-64a^3{x}^3}{y}$$	[_rational]	✓	✓
$334$	10875	$$y^{\prime }=-\frac{-xy-y+\sqrt{x^2+y^2}{x}^2-x\sqrt{x^2+y^2}y}{x(x+1)}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$335$	10879	$$y^{\prime }=\frac{(a^3+y^4{a}^3+2y^2{a}^{2}b{x}^2+a{x}^4{b}^2+y^6{a}^3+3y^4{a}^{2}b{x}^2+3y^{2}a{b}^2{x}^4+b^3{x}^6)x}{a^{7/2}y}$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$336$	10880	$$y^{\prime }=-\frac{(-1-y^4+2x^2{y}^2-x^4-y^6+3x^2{y}^4-3x^4{y}^2+x^6)x}{y}$$	[_rational]	✓	✓
$337$	10885	$$y^{\prime }=-\frac{(-8-8y^3+24y^{3/2}{\mathrm{e}}^x-18{\mathrm{e}}^{2x}-8y^{9/2}+36y^3{\mathrm{e}}^x-54y^{3/2}{\mathrm{e}}^{2x}+27{\mathrm{e}}^{3x}){\mathrm{e}}^x}{8\sqrt{y}}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$338$	10886	$$y^{\prime }=\frac{x}{-y+1+y^4+2x^2{y}^2+x^4+y^6+3x^2{y}^4+3x^4{y}^2+x^6}$$	[_rational]	✓	✓
$339$	10887	$$y^{\prime }=\frac{y^2(-2y+2x^2+2x^{2}y+y{x}^4)}{x^3(x^2-y+x^{2}y)}$$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	✓
$340$	10891	$$y^{\prime }=\frac{(-256a{x}^{2}y-32a^2{x}^6-256a{x}^2+512y^3+192x^{4}a{y}^2+24y{a}^2{x}^8+a^3{x}^{12})x}{512y+64a{x}^4+512}$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	✓
$341$	10892	$$y^{\prime }=\frac{x+1+y^4-2x^2{y}^2+x^4+y^6-3x^2{y}^4+3x^4{y}^2-x^6}{y}$$	[_rational]	✓	✓
$342$	10893	$$y^{\prime }=\frac{(-108x^{3/2}y+18x^{9/2}-108x^{3/2}-216y^3+108x^3{y}^2-18x^{6}y+x^9)\sqrt{x}}{-216y+36x^3-216}$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	✓
$343$	10894	$$y^{\prime }=\frac{32x^{5}y+8x^3+32x^5+64x^6{y}^3+48x^4{y}^2+12x^{2}y+1}{16x^6(4x^{2}y+1+4x^2)}$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	✓
$344$	10898	$$y^{\prime }=\frac{-x{y}^2+x^3-x-y^6+3x^2{y}^4-3x^4{y}^2+x^6}{(-y^2+x^2-1)y}$$	[_rational]	✓	✓
$345$	10902	$$y^{\prime }=\frac{x(x^2+y^2+1)}{-y^3-x^{2}y-y+y^6+3x^2{y}^4+3x^4{y}^2+x^6}$$	[_rational]	✓	✓
$346$	10904	$$y^{\prime }=\frac{4x(a-1)(a+1)}{4y+a^2{y}^4-2a^4{y}^2{x}^2+4y^2{a}^2{x}^2+a^6{x}^4-3a^4{x}^4+3a^2{x}^4-y^4-2x^2{y}^2-x^4}$$	[_rational]	✓	✓
$347$	10905	$$y^{\prime }=\frac{x^3+y^4{x}^3+2x^2{y}^2+x+x^3{y}^6+3x^2{y}^4+3x{y}^2+1}{x^{5}y}$$	[_rational]	✓	✓
$348$	10906	$$y^{\prime }=\frac{-2x-y+1+x^2{y}^2+2x^{3}y+x^4+x^3{y}^3+3x^4{y}^2+3x^{5}y+x^6}{x}$$	[_rational, _Abel]	✓	✓
$349$	10912	$$y^{\prime }=\frac{y(\ln \left(y\right)x+\ln \left(y\right)-x-1+x\ln \left(x\right)+\ln \left(x\right)+x^4\ln {\left(x\right)}^2+2x^4\ln \left(y\right)\ln \left(x\right)+x^4\ln {\left(y\right)}^2)}{x(x+1)}$$	[NONE]	✓	✓
$350$	10913	$$y^{\prime }=\frac{y(x\ln \left(x\right)+\ln \left(x\right)+\ln \left(y\right)x+\ln \left(y\right)-x-1+x\ln {\left(x\right)}^2+2x\ln \left(y\right)\ln \left(x\right)+x\ln {\left(y\right)}^2)}{x(x+1)}$$	[NONE]	✓	✓
$351$	10924	$$y^{\prime }=\frac{({\mathrm{e}}^{-\frac{y}{x}}yx+{\mathrm{e}}^{-\frac{y}{x}}y+{\mathrm{e}}^{-\frac{y}{x}}{x}^2+{\mathrm{e}}^{-\frac{y}{x}}x+x){\mathrm{e}}^{\frac{y}{x}}}{x(x+1)}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$352$	10926	$$y^{\prime }=\frac{({\mathrm{e}}^{-\frac{y}{x}}yx+{\mathrm{e}}^{-\frac{y}{x}}y+{\mathrm{e}}^{-\frac{y}{x}}{x}^2+{\mathrm{e}}^{-\frac{y}{x}}x+x^4){\mathrm{e}}^{\frac{y}{x}}}{x(x+1)}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$353$	10928	$$y^{\prime }=\frac{(27y^3+27{\mathrm{e}}^{3x^2}y+18{\mathrm{e}}^{3x^2}{y}^2+3y^3{\mathrm{e}}^{3x^2}+27{\mathrm{e}}^{\frac{9x^2}{2}}+27{\mathrm{e}}^{\frac{9x^2}{2}}y+9{\mathrm{e}}^{\frac{9x^2}{2}}{y}^2+{\mathrm{e}}^{\frac{9x^2}{2}}{y}^3){\mathrm{e}}^{3x^2}x{\mathrm{e}}^{-\frac{9x^2}{2}}}{243y}$$	[[_Abel, ‘2nd type‘, ‘class C‘]]	✓	✓
$354$	10929	$$y^{\prime }=-\frac{-x^2-xy-x^3-x{y}^2+2y{x}^2\ln \left(x\right)-x^3\ln {\left(x\right)}^2-y^3+3x{y}^2\ln \left(x\right)-3x^2\ln {\left(x\right)}^{2}y+x^3\ln {\left(x\right)}^3}{x^2}$$	[_Abel]	✓	✓
$355$	10933	$$y^{\prime }=\frac{-2y-2\ln (2x+1)-2+2x{y}^3+y^3+6y^2\ln (2x+1)x+3y^2\ln (2x+1)+6y\ln {(2x+1)}^{2}x+3y\ln {(2x+1)}^2+2\ln {(2x+1)}^{3}x+\ln {(2x+1)}^3}{(2x+1)(y+\ln (2x+1)+1)}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	✓
$356$	10936	$$y^{\prime }=\frac{y\ln \left(x\right)x+x^2\ln \left(x\right)-2xy-x^2-y^2-y^3+3x{y}^2\ln \left(x\right)-3x^2\ln {\left(x\right)}^{2}y+x^3\ln {\left(x\right)}^3}{x(-y+x\ln \left(x\right)-x)}$$	[[_Abel, ‘2nd type‘, ‘class C‘], [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$357$	10942	$$y^{\prime }=\frac{(-8{\mathrm{e}}^{-x^2}y+4x^2{\mathrm{e}}^{-2x^2}-8{\mathrm{e}}^{-x^2}+8x^2{\mathrm{e}}^{-x^2}y-4x^4{\mathrm{e}}^{-2x^2}+8x^2{\mathrm{e}}^{-x^2}-8y^3+12x^2{\mathrm{e}}^{-x^2}{y}^2-6y{x}^4{\mathrm{e}}^{-2x^2}+x^6{\mathrm{e}}^{-3x^2})x}{-8y+4x^2{\mathrm{e}}^{-x^2}-8}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class C‘]]	✓	✓
$358$	10948	$$y^{\prime }=-\frac{-y+\sqrt{x^2+y^2}{x}^2-x\sqrt{x^2+y^2}y+x^4\sqrt{x^2+y^2}-x^3\sqrt{x^2+y^2}y+x^5\sqrt{x^2+y^2}-x^4\sqrt{x^2+y^2}y}{x}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$359$	10949	$$y^{\prime }=\frac{y(\ln \left(x\right)+\ln \left(y\right)-1+x\ln {\left(x\right)}^2+2x\ln \left(y\right)\ln \left(x\right)+x\ln {\left(y\right)}^2+x^3\ln {\left(x\right)}^2+2x^3\ln \left(y\right)\ln \left(x\right)+x^3\ln {\left(y\right)}^2+x^4\ln {\left(x\right)}^2+2x^4\ln \left(y\right)\ln \left(x\right)+x^4\ln {\left(y\right)}^2)}{x}$$	[NONE]	✓	✓
$360$	10951	$$y^{\prime }=\frac{-150x^{3}y+60x^6+350x^{7/2}-150x^3-125y\sqrt{x}+250x-125\sqrt{x}-125y^3+150x^3{y}^2+750y^2\sqrt{x}-60x^{6}y-600y{x}^{7/2}-1500xy+8x^9+120x^{13/2}+600x^4+1000x^{3/2}}{25(-5y+2x^3+10\sqrt{x}-5)x}$$	[_rational, [_Abel, ‘2nd type‘, ‘class C‘]]	✓	✓
$361$	10952	$$y^{\prime }=\frac{y(-1-x^{\frac{2}{1+\ln \left(x\right)}}{\mathrm{e}}^{\frac{2\ln {\left(x\right)}^2}{1+\ln \left(x\right)}}{x}^2-x^{\frac{2}{1+\ln \left(x\right)}}{\mathrm{e}}^{\frac{2\ln {\left(x\right)}^2}{1+\ln \left(x\right)}}{x}^2\ln \left(x\right)+x^{\frac{2}{1+\ln \left(x\right)}}{\mathrm{e}}^{\frac{2\ln {\left(x\right)}^2}{1+\ln \left(x\right)}}{x}^{2}y+2x^{\frac{2}{1+\ln \left(x\right)}}{\mathrm{e}}^{\frac{2\ln {\left(x\right)}^2}{1+\ln \left(x\right)}}{x}^{2}y\ln \left(x\right)+x^{\frac{2}{1+\ln \left(x\right)}}{\mathrm{e}}^{\frac{2\ln {\left(x\right)}^2}{1+\ln \left(x\right)}}{x}^{2}y\ln {\left(x\right)}^2)}{(1+\ln \left(x\right))x}$$	[_Bernoulli]	✓	✓
$362$	10953	$$y^{\prime }=\frac{y(-1-x^3{x}^{\frac{2}{1+\ln \left(x\right)}}{\mathrm{e}}^{\frac{2\ln {\left(x\right)}^2}{1+\ln \left(x\right)}}-x^3{x}^{\frac{2}{1+\ln \left(x\right)}}{\mathrm{e}}^{\frac{2\ln {\left(x\right)}^2}{1+\ln \left(x\right)}}\ln \left(x\right)+x^3{x}^{\frac{2}{1+\ln \left(x\right)}}{\mathrm{e}}^{\frac{2\ln {\left(x\right)}^2}{1+\ln \left(x\right)}}y+2x^3{x}^{\frac{2}{1+\ln \left(x\right)}}{\mathrm{e}}^{\frac{2\ln {\left(x\right)}^2}{1+\ln \left(x\right)}}y\ln \left(x\right)+x^3{x}^{\frac{2}{1+\ln \left(x\right)}}{\mathrm{e}}^{\frac{2\ln {\left(x\right)}^2}{1+\ln \left(x\right)}}y\ln {\left(x\right)}^2)}{(1+\ln \left(x\right))x}$$	[_Bernoulli]	✓	✓
$363$	10958	$$y^{\prime }=\frac{4x(a-1)(a+1)(-y^2+a^2{x}^2-x^2-2)}{-4y^3+4a^2{x}^{2}y-4x^{2}y-8y-a^2{y}^6+3a^4{y}^4{x}^2-6y^4{a}^2{x}^2-3a^6{y}^2{x}^4+9y^2{a}^4{x}^4-9y^2{a}^2{x}^4+a^8{x}^6-4a^6{x}^6+6a^4{x}^6-4a^2{x}^6+y^6+3x^2{y}^4+3x^4{y}^2+x^6}$$	[_rational]	✓	✓
$364$	10960	$$y^{\prime }=-\frac{8x(a-1)(a+1)}{8+3x^2{y}^4-a^2{y}^6+a^8{x}^6-4a^6{x}^6+6a^4{x}^6+3a^4{y}^4{x}^2-6y^4{a}^2{x}^2-3a^6{y}^2{x}^4+9y^2{a}^4{x}^4-9y^2{a}^2{x}^4+3x^4{y}^2-4a^2{x}^6-2a^2{y}^4-2a^6{x}^4+6a^4{x}^4-6a^2{x}^4-8y^2{a}^2{x}^2+4a^4{y}^2{x}^2+2y^4-8a^2+4x^2{y}^2+y^6+2x^4-8y+x^6}$$	[_rational]	✓	✓
$365$	10966	$$y^{\prime }=-\frac{216y(-2y^4-3y^3-6y^2-6y+6x+6)}{-216x^2{y}^4-1944x{y}^2-648x^{2}y+1728y^3-324x^2{y}^3-1296xy-18y^8+594y^7-126y^{10}-315y^9-8y^{12}-36y^{11}-1296y^2+72y^{8}x+2808y^4+4428y^5-648x{y}^3-648x^2{y}^2+216y^{7}x+1080y^{5}x+594x{y}^6-432x{y}^4+2484y^6+216x^3-1296y}$$	[_rational]	✓	✓
$366$	10968	$$y^{\prime }=\frac{x(-x^2+2x^{2}y-2x^4+1)}{y-x^2}$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓
$367$	10972	$$y^{\prime }=\frac{y(y^2{x}^7+y{x}^4+x-3)}{x}$$	[_rational, _Abel]	✓	✓
$368$	10980	$$y^{\prime }=\frac{y(x^2{y}^2+yx{\mathrm{e}}^x+{\mathrm{e}}^{2x}){\mathrm{e}}^{-2x}(x-1)}{x}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _Abel]	✓	✓
$369$	11008	$$y^{\prime \prime }-(x^2+a)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$370$	11012	$$y^{\prime \prime }+(a{x}^{2c}+b{x}^{c-1})y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$371$	11016	$$y^{\prime \prime }+(a{\mathrm{e}}^{2x}+b{\mathrm{e}}^x+c)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$372$	11017	$$y^{\prime \prime }+(a\cosh {\left(x\right)}^2+b)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$373$	11018	$$y^{\prime \prime }+(a\cos \left(2x\right)+b)y=0$$	[_ellipsoidal]	✓	✓
$374$	11019	$$y^{\prime \prime }+(a\cos {\left(x\right)}^2+b)y=0$$	[_ellipsoidal]	✓	✓
$375$	11020	$$y^{\prime \prime }-(1+2\tan {\left(x\right)}^2)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$376$	11021	$$y^{\prime \prime }-(\frac{m(m-1)}{\cos {\left(x\right)}^2}+\frac{n(n-1)}{\sin {\left(x\right)}^2}+a)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$377$	11022	$$y^{\prime \prime }-(n(n+1)k^2\mathrm{JacobiSN}{(x,k)}^2+b)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$378$	11023	$$y^{\prime \prime }-(f{\left(x\right)}^2+f^{\prime }\left(x\right))y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$379$	11028	$$y^{\prime \prime }+a{y}^{\prime }-(b^2{x}^2+c)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$380$	11032	$$y^{\prime \prime }+y^{\prime }x+(n+1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$381$	11033	$$y^{\prime \prime }+y^{\prime }x-ny=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$382$	11035	$$y^{\prime \prime }-y^{\prime }x-ay=0$$	[_Hermite]	✓	✓
$383$	11037	$$y^{\prime \prime }-2y^{\prime }x+ay=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$384$	11039	$$y^{\prime \prime }-4y^{\prime }x+(3x^2+2n-1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$385$	11043	$$y^{\prime \prime }+ax{y}^{\prime }+by=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$386$	11045	$$y^{\prime \prime }+(ax+b)y^{\prime }+(cx+d)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$387$	11046	$$y^{\prime \prime }+(ax+b)y^{\prime }+(\mathrm{a}1x^2+\mathrm{b}1x+\mathrm{c}1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$388$	11051	$$y^{\prime \prime }+a{x}^{q-1}{y}^{\prime }+b{x}^{q-2}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$389$	11056	$$y^{\prime \prime }+2n{y}^{\prime }\cot \left(x\right)+(-a^2+n^2)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$390$	11059	$$y^{\prime \prime }+\cot \left(x\right)y^{\prime }+v(v+1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$391$	11061	$$y^{\prime \prime }+a{y}^{\prime }\tan \left(x\right)+by=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$392$	11065	$$y^{\prime \prime }-(\frac{f^{\prime }\left(x\right)}{f\left(x\right)}+2a)y^{\prime }+(\frac{a{f}^{\prime }\left(x\right)}{f\left(x\right)}+a^2-b^{2}f{\left(x\right)}^2)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$393$	11066	$$y^{\prime \prime }-(\frac{2f^{\prime }\left(x\right)}{f\left(x\right)}+\frac{g^{\prime \prime }\left(x\right)}{g^{\prime }\left(x\right)}-\frac{g^{\prime }\left(x\right)}{g\left(x\right)})y^{\prime }+(\frac{f^{\prime }\left(x\right)(\frac{2f^{\prime }\left(x\right)}{f\left(x\right)}+\frac{g^{\prime \prime }\left(x\right)}{g^{\prime }\left(x\right)}-\frac{g^{\prime }\left(x\right)}{g\left(x\right)})}{f\left(x\right)}-\frac{f^{\prime \prime }\left(x\right)}{f\left(x\right)}-\frac{v^2{g^{\prime }\left(x\right)}^2}{g{\left(x\right)}^2}+{g^{\prime }\left(x\right)}^2)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$394$	11067	$$y^{\prime \prime }-(\frac{g^{\prime \prime }\left(x\right)}{g^{\prime }\left(x\right)}+\frac{(2v-1)g^{\prime }\left(x\right)}{g\left(x\right)}+\frac{2h^{\prime }\left(x\right)}{h\left(x\right)})y^{\prime }+(\frac{h^{\prime }\left(x\right)(\frac{g^{\prime \prime }\left(x\right)}{g^{\prime }\left(x\right)}+\frac{(2v-1)g^{\prime }\left(x\right)}{g\left(x\right)}+\frac{2h^{\prime }\left(x\right)}{h\left(x\right)})}{h\left(x\right)}-\frac{h^{\prime \prime }\left(x\right)}{h\left(x\right)}+{g^{\prime }\left(x\right)}^2)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$395$	11069	$$4y^{\prime \prime }-(x^2+a)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$396$	11070	$$4y^{\prime \prime }+4y^{\prime }\tan \left(x\right)-(5\tan {\left(x\right)}^2+2)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$397$	11071	$$a{y}^{\prime \prime }-(ab+c+x)y^{\prime }+(b(x+c)+d)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$398$	11074	$$x{y}^{\prime \prime }+(x+a)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$399$	11078	$$x{y}^{\prime \prime }+y^{\prime }+(x+a)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$400$	11081	$$x{y}^{\prime \prime }-y^{\prime }+x^3({\mathrm{e}}^{x^2}-v^2)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$401$	11089	$$x{y}^{\prime \prime }+(x+b)y^{\prime }+ay=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$402$	11090	$$x{y}^{\prime \prime }+(x+a+b)y^{\prime }+ay=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$403$	11092	$$x{y}^{\prime \prime }-y^{\prime }x-ay=0$$	[_Laguerre]	✓	✓
$404$	11095	$$x{y}^{\prime \prime }+(b-x)y^{\prime }-ay=0$$	[_Laguerre]	✓	✓
$405$	11096	$$x{y}^{\prime \prime }-2(x-1)y^{\prime }-y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$406$	11097	$$x{y}^{\prime \prime }-(3x-2)y^{\prime }-(2x-3)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$407$	11098	$$x{y}^{\prime \prime }+(ax+b+n)y^{\prime }+nay=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$408$	11099	$$x{y}^{\prime \prime }-(a+b)(x+1)y^{\prime }+abxy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$409$	11100	$$x{y}^{\prime \prime }+((a+b)x+m+n)y^{\prime }+(abx+an+bm)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$410$	11102	$$x{y}^{\prime \prime }+(ax+b)y^{\prime }+(cx+d)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$411$	11106	$$x{y}^{\prime \prime }-2(x^2-a)y^{\prime }+2nxy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$412$	11110	$$x{y}^{\prime \prime }+(f\left(x\right)x+2)y^{\prime }+f\left(x\right)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$413$	11113	$$2x{y}^{\prime \prime }-(x-1)y^{\prime }+ay=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$414$	11114	$$2x{y}^{\prime \prime }-(2x-1)y^{\prime }+ay=0$$	[_Laguerre]	✓	✓
$415$	11116	$$4x{y}^{\prime \prime }-(x+a)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$416$	11119	$$4x{y}^{\prime \prime }+4y-(x+2)y+ly=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$417$	11120	$$4x{y}^{\prime \prime }+4m{y}^{\prime }-(x-2m-4n)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$418$	11121	$$16x{y}^{\prime \prime }+8y^{\prime }-(x+a)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$419$	11123	$$ax{y}^{\prime \prime }+(bx+3a)y^{\prime }+3by=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$420$	11124	$$5(ax+b)y^{\prime \prime }+8a{y}^{\prime }+c{(ax+b)}^{1/5}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$421$	11125	$$2ax{y}^{\prime \prime }+(bx+a)y^{\prime }+cy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$422$	11126	$$2ax{y}^{\prime \prime }+(bx+3a)y^{\prime }+cy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$423$	11127	$$(\mathrm{a}2x+\mathrm{b}2)y^{\prime \prime }+(\mathrm{a}1x+\mathrm{b}1)y^{\prime }+(\mathrm{a}0x+\mathrm{b}0)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$424$	11136	$$x^2{y}^{\prime \prime }+(a{x}^2+bx+c)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$425$	11138	$$x^2{y}^{\prime \prime }+\frac{y}{\ln \left(x\right)}-x{\mathrm{e}}^x(2+x\ln \left(x\right))=0$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$426$	11153	$$x^2{y}^{\prime \prime }+2y^{\prime }x+(l{x}^2+ax-n(n+1))y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$427$	11154	$$x^2{y}^{\prime \prime }+2(x-1)y^{\prime }+ay=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$428$	11155	$$x^2{y}^{\prime \prime }+2(x+a)y^{\prime }-b(b-1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$429$	11170	$$x^2{y}^{\prime \prime }+(ax+b)y^{\prime }+cy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$430$	11172	$$x^2{y}^{\prime \prime }+x^2{y}^{\prime }+(ax+b)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$431$	11177	$$x^2{y}^{\prime \prime }+(3+x)x{y}^{\prime }-y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$432$	11179	$$x^2{y}^{\prime \prime }-(x^2-2x)y^{\prime }-(x+a)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$433$	11182	$$x^2{y}^{\prime \prime }+2x^2{y}^{\prime }-v(v-1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$434$	11188	$$x^2{y}^{\prime \prime }+(2ax+b)x{y}^{\prime }+(abx+c{x}^2+d)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$435$	11189	$$x^2{y}^{\prime \prime }+(ax+b)y^{\prime }x+(\mathrm{a}1x^2+\mathrm{b}1x+\mathrm{c}1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$436$	11192	$$x^2{y}^{\prime \prime }-2x(x^2-a)y^{\prime }+(2n{x}^2+({(-1)}^n-1)a)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$437$	11195	$$x^2{y}^{\prime \prime }+(x^3+1)x{y}^{\prime }-y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$438$	11196	$$x^2{y}^{\prime \prime }+(-x^4+(2n+2a+1)x^2+{(-1)}^{n}a-a^2)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$439$	11197	$$x^2{y}^{\prime \prime }+(a{x}^n+b)y^{\prime }x+(\mathrm{a}1x^{2n}+\mathrm{b}1x^n+\mathrm{c}1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$440$	11198	$$x^2{y}^{\prime \prime }-(2x^2\tan \left(x\right)-x)y^{\prime }-(x\tan \left(x\right)+a)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$441$	11199	$$x^2{y}^{\prime \prime }+(2x^2\cot \left(x\right)+x)y^{\prime }+(x\cot \left(x\right)+a)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$442$	11200	$$x^2{y}^{\prime \prime }+2xf\left(x\right)y^{\prime }+(f^{\prime }\left(x\right)x+f{\left(x\right)}^2-f\left(x\right)+a{x}^2+bx+c)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$443$	11201	$$x^2{y}^{\prime \prime }+2x^{2}f\left(x\right)y^{\prime }+(x^2(f^{\prime }\left(x\right)+f{\left(x\right)}^2+a)-v(v-1))y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$444$	11202	$$x^2{y}^{\prime \prime }+(x-2x^{2}f\left(x\right))y^{\prime }+(x^2(1+f{\left(x\right)}^2-f^{\prime }\left(x\right))-f\left(x\right)x-v^2)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$445$	11207	$$(x^2+1)y^{\prime \prime }+2y^{\prime }x-v(v-1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$446$	11212	$$(x^2-1)y^{\prime \prime }-v(v+1)y=0$$	[_Gegenbauer]	✓	✓
$447$	11213	$$(x^2-1)y^{\prime \prime }-n(n+1)y+\frac{d}{dx}\mathrm{LegendreP}(n,x)=0$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$448$	11219	$$(x^2-1)y^{\prime \prime }+2y^{\prime }x-ly=0$$	[_Gegenbauer]	✓	✓
$449$	11220	$$(x^2-1)y^{\prime \prime }+2y^{\prime }x-v(v+1)y=0$$	[_Gegenbauer]	✓	✓
$450$	11221	$$(x^2-1)y^{\prime \prime }-2y^{\prime }x-(v+2)(v-1)y=0$$	[_Gegenbauer]	✓	✓
$451$	11224	$$(x^2-1)y^{\prime \prime }+2(n+1)x{y}^{\prime }-(v+n+1)(v-n)y=0$$	[_Gegenbauer]	✓	✓
$452$	11225	$$(x^2-1)y^{\prime \prime }-2(n-1)x{y}^{\prime }-(v-n+1)(v+n)y=0$$	[_Gegenbauer]	✓	✓
$453$	11228	$$(x^2-1)y^{\prime \prime }+ax{y}^{\prime }+(b{x}^2+cx+d)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$454$	11229	$$(x^2-1)y^{\prime \prime }+(ax+b)y^{\prime }+cy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$455$	11232	$$x(x+1)y^{\prime \prime }+(ax+b)y^{\prime }+cy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$456$	11236	$$x(x-1)y^{\prime \prime }+(2x-1)y^{\prime }-v(v+1)y=0$$	[_Jacobi]	✓	✓
$457$	11238	$$x(x-1)y^{\prime \prime }+(ax+b)y^{\prime }+cy=0$$	[_Jacobi]	✓	✓
$458$	11239	$$x(x-1)y^{\prime \prime }+((a+1)x+b)y^{\prime }-ly=0$$	[_Jacobi]	✓	✓
$459$	11241	$$x(x+2)y^{\prime \prime }+2(n+1+(n+1-2l)x-l{x}^2)y^{\prime }+(2l(p-n-1)x+2pl+m)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$460$	11245	$$(x-1)(x-2)y^{\prime \prime }-(2x-3)y^{\prime }+y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$461$	11248	$$2x(x-1)y^{\prime \prime }+(2x-1)y^{\prime }+(ax+b)y=0$$	[_Jacobi]	✓	✓
$462$	11249	$$2x(x-1)y^{\prime \prime }+((2v+5)x-2v-3)y^{\prime }+(v+1)y=0$$	[_Jacobi]	✓	✓
$463$	11253	$$4x^2{y}^{\prime \prime }-(-4kx+4m^2+x^2-1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$464$	11255	$$4x^2{y}^{\prime \prime }+4y^{\prime }x+(-x^2+2(1-m+2l)x-m^2+1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$465$	11265	$$x(4x-1)y^{\prime \prime }+((4a+2)x-a)y^{\prime }+a(a-1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$466$	11271	$$48x(x-1)y^{\prime \prime }+(152x-40)y^{\prime }+53y=0$$	[_Jacobi]	✓	✓
$467$	11273	$$144x(x-1)y^{\prime \prime }+(120x-48)y^{\prime }+y=0$$	[_Jacobi]	✓	✓
$468$	11274	$$144x(x-1)y^{\prime \prime }+(168x-96)y^{\prime }+y=0$$	[_Jacobi]	✓	✓
$469$	11275	$$a{x}^2{y}^{\prime \prime }+bx{y}^{\prime }+(c{x}^2+dx+f)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$470$	11276	$$\mathrm{a}2x^2{y}^{\prime \prime }+(\mathrm{a}1x^2+\mathrm{b}1x)y^{\prime }+(\mathrm{a}0x^2+\mathrm{b}0x+\mathrm{c}0)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$471$	11281	$$\mathrm{A}2{(ax+b)}^2{y}^{\prime \prime }+\mathrm{A}1(ax+b)y^{\prime }+\mathrm{A}0(ax+b)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$472$	11282	$$(a{x}^2+bx+c)y^{\prime \prime }+(dx+f)y^{\prime }+gy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$473$	11284	$$x^3{y}^{\prime \prime }+2y^{\prime }x-y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$474$	11285	$$x^3{y}^{\prime \prime }+x^2{y}^{\prime }+(a{x}^2+bx+a)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$475$	11288	$$x^3{y}^{\prime \prime }-(x^2-1)y^{\prime }+xy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$476$	11290	$$x(x^2+1)y^{\prime \prime }+(2x^2+1)y^{\prime }-v(v+1)xy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$477$	11292	$$x(x^2+1)y^{\prime \prime }+(2(n+1)x^2+2n+1)y^{\prime }-(v-n)(v+n+1)xy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$478$	11293	$$x(x^2+1)y^{\prime \prime }-(2(n-1)x^2+2n-1)y^{\prime }+(v+n)(-v+n-1)xy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$479$	11295	$$x(x^2-1)y^{\prime \prime }+(x^2-1)y^{\prime }-xy=0$$	[[_elliptic, _class_II]]	✓	✓
$480$	11296	$$x(x^2-1)y^{\prime \prime }+(3x^2-1)y^{\prime }+xy=0$$	[[_elliptic, _class_I]]	✓	✓
$481$	11297	$$x(x^2-1)y^{\prime \prime }+(a{x}^2+b)y^{\prime }+cxy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$482$	11304	$$y^{\prime \prime }=-\frac{((a+b+1)x+\alpha +\beta -1)y^{\prime }}{x(x-1)}-\frac{(abx-\alpha \beta )y}{x^2(x-1)}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$483$	11306	$$y^{\prime \prime }=\frac{2y^{\prime }}{x(x-2)}-\frac{y}{x^2(x-2)}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$484$	11308	$$y^{\prime \prime }=-\frac{((\alpha +\beta +1)x^2-(\alpha +\beta +1+a(\gamma +\delta )-\delta )x+a\gamma )y^{\prime }}{x(x-1)(x-a)}-\frac{(\alpha \beta x-q)y}{x(x-1)(x-a)}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$485$	11309	$$y^{\prime \prime }=-\frac{(A{x}^2+Bx+C)y^{\prime }}{(x-a)(x-b)(x-c)}-\frac{(\mathrm{DD}x+E)y}{(x-a)(x-b)(x-c)}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$486$	11312	$$y^{\prime \prime }=-\frac{(3x-1)y^{\prime }}{2x(x-1)}+\frac{v(v+1)y}{4x^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$487$	11313	$$y^{\prime \prime }=-\frac{((a+1)x-1)y^{\prime }}{x(x-1)}-\frac{((a^2-b^2)x+c^2)y}{4x^2(x-1)}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$488$	11314	$$y^{\prime \prime }=-\frac{(3x-1)y^{\prime }}{2x(x-1)}-\frac{(ax+b)y}{4x{(x-1)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$489$	11318	$$y^{\prime \prime }=-\frac{(a(b+2)x^2+(c-d+1)x)y^{\prime }}{(ax+1)x^2}-\frac{(abx-cd)y}{(ax+1)x^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$490$	11320	$$y^{\prime \prime }=-\frac{(2ax+b)y^{\prime }}{x(ax+b)}-\frac{(avx-b)y}{(ax+b)x^2}+Ax$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$491$	11322	$$y^{\prime \prime }=-\frac{(x^{2}a(1-a)-b(x+b))y}{x^4}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$492$	11323	$$y^{\prime \prime }=-\frac{({\mathrm{e}}^{\frac{2}{x}}-v^2)y}{x^4}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$493$	11327	$$y^{\prime \prime }=-\frac{y^{\prime }}{x}-\frac{(b{x}^2+a(x^4+1))y}{x^4}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$494$	11328	$$y^{\prime \prime }=-\frac{(x^2+1)y^{\prime }}{x^3}-\frac{y}{x^4}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$495$	11335	$$y^{\prime \prime }=-\frac{(2x^2+1)y^{\prime }}{x(x^2+1)}-\frac{(-v(v+1)x^2-n^2)y}{x^2(x^2+1)}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$496$	11336	$$y^{\prime \prime }=-\frac{(a{x}^2+a-1)y^{\prime }}{x(x^2+1)}-\frac{(b{x}^2+c)y}{x^2(x^2+1)}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$497$	11338	$$y^{\prime \prime }=-\frac{2x{y}^{\prime }}{x^2-1}-\frac{v(v+1)y}{x^2(x^2-1)}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$498$	11339	$$y^{\prime \prime }=-\frac{2x{y}^{\prime }}{x^2-1}+\frac{v(v+1)y}{x^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$499$	11341	$$x^2(x^2-1)y^{\prime \prime }-2x^3{y}^{\prime }-((a-n)(a+n+1)x^2(x^2-1)+2a{x}^2+n(n+1)(x^2-1))y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$500$	11342	$$y^{\prime \prime }=-\frac{(a{x}^2+a-2)y^{\prime }}{x(x^2-1)}-\frac{by}{x^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$501$	11343	$$y^{\prime \prime }=\frac{(2bc{x}^c(x^2-1)+2(a-1)x^2-2a)y^{\prime }}{x(x^2-1)}-\frac{(b^2{c}^2{x}^{2c}(x^2-1)+bc{x}^{c+2}(2a-c-1)-bc{x}^c(2a-c+1)+x^2(a(a-1)-v(v+1))-a(a+1))y}{x^2(x^2-1)}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$502$	11346	$$y^{\prime \prime }=-\frac{2x{y}^{\prime }}{x^2+1}-\frac{(a^2{(x^2+1)}^2-n(n+1)(x^2+1)+m^2)y}{{(x^2+1)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$503$	11347	$$y^{\prime \prime }=-\frac{ax{y}^{\prime }}{x^2+1}-\frac{by}{{(x^2+1)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$504$	11350	$$y^{\prime \prime }=-\frac{2x{y}^{\prime }}{x^2-1}-\frac{(-a^2-\lambda (x^2-1))y}{{(x^2-1)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$505$	11351	$$y^{\prime \prime }=-\frac{2x{y}^{\prime }}{x^2-1}-\frac{((x^2-1)(a{x}^2+bx+c)-k^2)y}{{(x^2-1)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$506$	11352	$$y^{\prime \prime }=-\frac{2x{y}^{\prime }}{x^2-1}-\frac{(-a^2{(x^2-1)}^2-n(n+1)(x^2-1)-m^2)y}{{(x^2-1)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$507$	11353	$$y^{\prime \prime }=\frac{2x(2a-1)y^{\prime }}{x^2-1}-\frac{(x^2(2a(2a-1)-v(v+1))+2a+v(v+1))y}{{(x^2-1)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$508$	11354	$$y^{\prime \prime }=-\frac{2x(n+1-2a)y^{\prime }}{x^2-1}-\frac{(4a{x}^2(a-n)-(x^2-1)(2a+(v-n)(v+n+1)))y}{{(x^2-1)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$509$	11363	$$y^{\prime \prime }=-\frac{(-x^2(a^2-1)+2(a+3)bx-b^2)y}{4x^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$510$	11367	$$y^{\prime \prime }=-\frac{(3x-1)y^{\prime }}{2x(x-1)}-\frac{(v(v+1)(x-1)-a^{2}x)y}{4x^2{(x-1)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$511$	11368	$$y^{\prime \prime }=-\frac{(3x-1)y^{\prime }}{2x(x-1)}-\frac{(-v(v+1){(x-1)}^2-4n^{2}x)y}{4x^2{(x-1)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$512$	11371	$$y^{\prime \prime }=-\frac{bx{y}^{\prime }}{(x^2-1)a}-\frac{(c{x}^2+dx+e)y}{a{(x^2-1)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$513$	11372	$$y^{\prime \prime }=-\frac{(b{x}^2+cx+d)y}{a{x}^2{(x-1)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$514$	11377	$$y^{\prime \prime }=-\frac{(3x^2-1)y^{\prime }}{(x^2-1)x}-\frac{(x^2-1-{(2v+1)}^2)y}{{(x^2-1)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$515$	11381	$$y^{\prime \prime }=-\frac{((1-4a)x^2-1)y^{\prime }}{x(x^2-1)}-\frac{((-v^2+x^2){(x^2-1)}^2+4a(a+1)x^4-2a{x}^2(x^2-1))y}{x^2{(x^2-1)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$516$	11382	$$y^{\prime \prime }=-(\frac{1-\mathrm{a}1-\mathrm{b}1}{x-\mathrm{c}1}+\frac{1-\mathrm{a}2-\mathrm{b}2}{x-\mathrm{c}2}+\frac{1-\mathrm{a}3-\mathrm{b}3}{x-\mathrm{c}3})y^{\prime }-\frac{(\frac{\mathrm{a}1\mathrm{b}1(\mathrm{c}1-\mathrm{c}3)(\mathrm{c}1-\mathrm{c}2)}{x-\mathrm{c}1}+\frac{\mathrm{a}2\mathrm{b}2(\mathrm{c}2-\mathrm{c}1)(\mathrm{c}2-\mathrm{c}3)}{x-\mathrm{c}2}+\frac{\mathrm{a}3\mathrm{b}3(\mathrm{c}3-\mathrm{c}2)(\mathrm{c}3-\mathrm{c}1)}{x-\mathrm{c}3})y}{(x-\mathrm{c}1)(x-\mathrm{c}2)(x-\mathrm{c}3)}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$517$	11386	$$y^{\prime \prime }=-(\frac{(1-\mathrm{al}1-\mathrm{bl}1)\mathrm{b}1}{\mathrm{b}1x-\mathrm{a}1}+\frac{(1-\mathrm{al}2-\mathrm{bl}2)\mathrm{b}2}{\mathrm{b}2x-\mathrm{a}2}+\frac{(1-\mathrm{al}3-\mathrm{bl}3)\mathrm{b}3}{\mathrm{b}3x-\mathrm{a}3})y^{\prime }-\frac{(\frac{\mathrm{al}1\mathrm{bl}1(\mathrm{a}1\mathrm{b}2-\mathrm{a}2\mathrm{b}1)(-\mathrm{a}1\mathrm{b}3+\mathrm{a}3\mathrm{b}1)}{\mathrm{b}1x-\mathrm{a}1}+\frac{\mathrm{al}2\mathrm{bl}2(\mathrm{a}2\mathrm{b}3-\mathrm{a}3\mathrm{b}2)(\mathrm{a}1\mathrm{b}2-\mathrm{a}2\mathrm{b}1)}{\mathrm{b}2x-\mathrm{a}2}+\frac{\mathrm{al}3\mathrm{bl}3(-\mathrm{a}1\mathrm{b}3+\mathrm{a}3\mathrm{b}1)(\mathrm{a}2\mathrm{b}3-\mathrm{a}3\mathrm{b}2)}{\mathrm{b}3x-\mathrm{a}3})y}{(\mathrm{b}1x-\mathrm{a}1)(\mathrm{b}2x-\mathrm{a}2)(\mathrm{b}3x-\mathrm{a}3)}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$518$	11389	$$y^{\prime \prime }=-\frac{(ap{x}^b+q)y^{\prime }}{x(a{x}^b-1)}-\frac{(ar{x}^b+s)y}{x^2(a{x}^b-1)}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$519$	11390	$$y^{\prime \prime }=\frac{y}{{\mathrm{e}}^x+1}$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✓
$520$	11393	$$y^{\prime \prime }=-\frac{(-a^2\sinh {\left(x\right)}^2-n(n-1))y}{\sinh {\left(x\right)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$521$	11394	$$y^{\prime \prime }=-\frac{2n\cosh \left(x\right)y^{\prime }}{\sinh \left(x\right)}-(-a^2+n^2)y$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$522$	11395	$$y^{\prime \prime }=-\frac{(2n+1)\cos \left(x\right)y^{\prime }}{\sin \left(x\right)}-(v+n+1)(v-n)y$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$523$	11399	$$\cos {\left(x\right)}^2{y}^{\prime \prime }-(a\cos {\left(x\right)}^2+n(n-1))y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$524$	11401	$$y^{\prime \prime }=\frac{2y}{\sin {\left(x\right)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$525$	11402	$$y^{\prime \prime }=-\frac{ay}{\sin {\left(x\right)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$526$	11403	$$\sin {\left(x\right)}^2{y}^{\prime \prime }-(a\sin {\left(x\right)}^2+n(n-1))y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$527$	11404	$$y^{\prime \prime }=-\frac{(-a^2\cos {\left(x\right)}^2-(3-2a)\cos \left(x\right)-3+3a)y}{\sin {\left(x\right)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$528$	11405	$$\sin {\left(x\right)}^2{y}^{\prime \prime }-(a^2\cos {\left(x\right)}^2+b\cos \left(x\right)+\frac{b^2}{{(2a-3)}^2}+3a+2)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$529$	11406	$$y^{\prime \prime }=-\frac{(-(a^2{b}^2-{(a+1)}^2)\sin {\left(x\right)}^2-a(a+1)b\sin \left(2x\right)-a(a-1))y}{\sin {\left(x\right)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$530$	11407	$$y^{\prime \prime }=-\frac{(a\cos {\left(x\right)}^2+b\sin {\left(x\right)}^2+c)y}{\sin {\left(x\right)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$531$	11409	$$y^{\prime \prime }=-\frac{\cos \left(x\right)y^{\prime }}{\sin \left(x\right)}-\frac{(v(v+1)\sin {\left(x\right)}^2-n^2)y}{\sin {\left(x\right)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$532$	11410	$$y^{\prime \prime }=\frac{\cos \left(2x\right)y^{\prime }}{\sin \left(2x\right)}-2y$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$533$	11412	$$y^{\prime \prime }=-\frac{\sin \left(x\right)y^{\prime }}{\cos \left(x\right)}-\frac{(2x^2+x^2\sin {\left(x\right)}^2-24\cos {\left(x\right)}^2)y}{4x^2\cos {\left(x\right)}^2}+\sqrt{\cos \left(x\right)}$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$534$	11413	$$y^{\prime \prime }=-\frac{b\cos \left(x\right)y^{\prime }}{\sin \left(x\right)a}-\frac{(c\cos {\left(x\right)}^2+d\cos \left(x\right)+e)y}{a\sin {\left(x\right)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$535$	11414	$$y^{\prime \prime }=-\frac{4\sin \left(3x\right)y}{\sin {\left(x\right)}^3}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$536$	11415	$$y^{\prime \prime }=-\frac{(4v(v+1)\sin {\left(x\right)}^2-\cos {\left(x\right)}^2+2-4n^2)y}{4\sin {\left(x\right)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$537$	11417	$$y^{\prime \prime }=-\frac{(-a\cos {\left(x\right)}^2\sin {\left(x\right)}^2-m(m-1)\sin {\left(x\right)}^2-n(n-1)\cos {\left(x\right)}^2)y}{\cos {\left(x\right)}^2\sin {\left(x\right)}^2}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$538$	11418	$$y^{\prime \prime }=-\frac{x{y}^{\prime }}{f\left(x\right)}+\frac{y}{f\left(x\right)}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$539$	11420	$$y^{\prime \prime }=-\frac{(2f\left(x\right){g^{\prime }\left(x\right)}^{2}g\left(x\right)-(g{\left(x\right)}^2-1)(f\left(x\right)g^{\prime \prime }\left(x\right)+2f^{\prime }\left(x\right)g^{\prime }\left(x\right)))y^{\prime }}{f\left(x\right)g^{\prime }\left(x\right)(g{\left(x\right)}^2-1)}-\frac{((g{\left(x\right)}^2-1)(f^{\prime }\left(x\right)(f\left(x\right)g^{\prime \prime }\left(x\right)+2f^{\prime }\left(x\right)g^{\prime }\left(x\right))-f\left(x\right)f^{\prime \prime }\left(x\right)g^{\prime }\left(x\right))-(2f^{\prime }\left(x\right)g\left(x\right)+v(v+1)f\left(x\right)g^{\prime }\left(x\right))f\left(x\right){g^{\prime }\left(x\right)}^2)y}{f{\left(x\right)}^2{g}^{\prime }\left(x\right)(g{\left(x\right)}^2-1)}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$540$	11425	$$y^{\prime \prime \prime }+ya{x}^3-bx=0$$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	✓
$541$	11426	$$y^{\prime \prime \prime }-a{x}^{b}y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$542$	11429	$$y^{\prime \prime \prime }+2ax{y}^{\prime }+ay=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$543$	11430	$$y^{\prime \prime \prime }-x^2{y}^{\prime \prime }+(a+b-1)x{y}^{\prime }-bya=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$544$	11431	$$y^{\prime \prime \prime }+x^{2c-2}{y}^{\prime }+(c-1)x^{2c-3}y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$545$	11438	$$y^{\prime \prime \prime }-6x{y}^{\prime \prime }+2(4x^2+2a-1)y^{\prime }-8yax=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$546$	11439	$$y^{\prime \prime \prime }+3ax{y}^{\prime \prime }+3a^2{x}^2{y}^{\prime }+a^3{x}^{3}y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$547$	11441	$$y^{\prime \prime \prime }+f\left(x\right)y^{\prime \prime }+y^{\prime }+f\left(x\right)y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$548$	11442	$$y^{\prime \prime \prime }+f\left(x\right)(x^2{y}^{\prime \prime }-2y^{\prime }x+2y)=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$549$	11444	$$x{y}^{\prime \prime \prime }+3y^{\prime \prime }+xy=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$550$	11445	$$x{y}^{\prime \prime \prime }+3y^{\prime \prime }-a{x}^{2}y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$551$	11446	$$x{y}^{\prime \prime \prime }+(a+b)y^{\prime \prime }-y^{\prime }x-ay=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$552$	11447	$$x{y}^{\prime \prime \prime }-(x+2v)y^{\prime \prime }-(x-2v-1)y^{\prime }+(x-1)y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$553$	11449	$$2x{y}^{\prime \prime \prime }+3y^{\prime \prime }+yax-b=0$$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	✓
$554$	11450	$$2x{y}^{\prime \prime \prime }-4(x+\nu -1)y^{\prime \prime }+(2x+6\nu -5)y^{\prime }+(1-2\nu )y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$555$	11453	$$(2x-1)y^{\prime \prime \prime }-8y^{\prime }x+8y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$556$	11455	$$x^2{y}^{\prime \prime \prime }-6y^{\prime }+a{x}^{2}y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$557$	11459	$$x^2{y}^{\prime \prime \prime }-3(x-m)x{y}^{\prime \prime }+(2x^2+4(n-m)x+m(2m-1))y^{\prime }-2n(2x-2m+1)y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$558$	11460	$$x^2{y}^{\prime \prime \prime }+4x{y}^{\prime \prime }+(x^2+2)y^{\prime }+3xy-f\left(x\right)=0$$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	✓
$559$	11463	$$x^2{y}^{\prime \prime \prime }+6x{y}^{\prime \prime }+6y^{\prime }+a{x}^{2}y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$560$	11464	$$x^2{y}^{\prime \prime \prime }-3(p+q)x{y}^{\prime \prime }+3p(3q+1)y^{\prime }-x^{2}y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$561$	11465	$$x^2{y}^{\prime \prime \prime }-2(n+1)x{y}^{\prime \prime }+(a{x}^2+6n)y^{\prime }-2yax=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$562$	11466	$$x^2{y}^{\prime \prime \prime }-(x^2-2x)y^{\prime \prime }-(x^2+{\nu }^2-\frac{1}{4})y^{\prime }+(x^2-2x+{\nu }^2-\frac{1}{4})y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$563$	11467	$$x^2{y}^{\prime \prime \prime }-(x+\nu )x{y}^{\prime \prime }+\nu (2x+1)y^{\prime }-\nu (x+1)y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✗
$564$	11468	$$x^2{y}^{\prime \prime \prime }-2(x^2-x)y^{\prime \prime }+(x^2-2x+\frac{1}{4}-{\nu }^2)y^{\prime }+({\nu }^2-\frac{1}{4})y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$565$	11469	$$x^2{y}^{\prime \prime \prime }-(x^4-6x)y^{\prime \prime }-(2x^3-6)y^{\prime }+2x^{2}y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$566$	11471	$$(x^2+2)y^{\prime \prime \prime }-2x{y}^{\prime \prime }+(x^2+2)y^{\prime }-2xy=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$567$	11472	$$2x(x-1)y^{\prime \prime \prime }+3(2x-1)y^{\prime \prime }+(2ax+b)y^{\prime }+ay=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$568$	11473	$$x^3{y}^{\prime \prime \prime }+(-{\nu }^2+1)x{y}^{\prime }+(a{x}^3+{\nu }^2-1)y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$569$	11474	$$x^3{y}^{\prime \prime \prime }+(4x^3+(-4{\nu }^2+1)x)y^{\prime }+(4{\nu }^2-1)y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$570$	11478	$$x^3{y}^{\prime \prime \prime }-4x^2{y}^{\prime \prime }+(x^2+8)x{y}^{\prime }-2(x^2+4)y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$571$	11481	$$x^3{y}^{\prime \prime \prime }+(3+x)x^2{y}^{\prime \prime }+5(x-6)x{y}^{\prime }+(4x+30)y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✗
$572$	11483	$$(x^2+1)x{y}^{\prime \prime \prime }+3(2x^2+1)y^{\prime \prime }-12y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$573$	11484	$$(3+x)x^2{y}^{\prime \prime \prime }-3x(x+2)y^{\prime \prime }+6(x+1)y^{\prime }-6y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$574$	11485	$$2(x-\mathrm{a}1)(x-\mathrm{a}2)(x-\mathrm{a}3)y^{\prime \prime \prime }+(9x^2-6(\mathrm{a}1+\mathrm{a}2+\mathrm{a}3)x+3\mathrm{a}1\mathrm{a}2+3\mathrm{a}1\mathrm{a}3+3\mathrm{a}2\mathrm{a}3)y^{\prime \prime }-2((n^2+n-3)x+b)y^{\prime }-n(n+1)y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$575$	11486	$$x^3(x+1)y^{\prime \prime \prime }-(2+4x)x^2{y}^{\prime \prime }+(4+10x)x{y}^{\prime }-4(3x+1)y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$576$	11488	$$x^3(x^2+1)y^{\prime \prime \prime }-(4x^2+2)x^2{y}^{\prime \prime }+(10x^2+4)x{y}^{\prime }-4(3x^2+1)y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$577$	11489	$$x^6{y}^{\prime \prime \prime }+x^2{y}^{\prime \prime }-2y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$578$	11490	$$x^6{y}^{\prime \prime \prime }+6x^5{y}^{\prime \prime }+ay=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$579$	11491	$$x^2(x^4+2x^2+2x+1)y^{\prime \prime \prime }-(2x^6+3x^4-6x^2-6x-1)y^{\prime \prime }+(x^6-6x^3-15x^2-12x-2)y^{\prime }+(x^4+4x^3+8x^2+6x+1)y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$580$	11492	$${(x-a)}^3{(x-b)}^3{y}^{\prime \prime \prime }-cy=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$581$	11495	$$y^{\prime \prime \prime }\sin {\left(x\right)}^2+3y^{\prime \prime }\sin \left(x\right)\cos \left(x\right)+(\cos \left(2x\right)+4\nu (\nu +1)\sin {\left(x\right)}^2)y^{\prime }+2\nu (\nu +1)y\sin \left(2x\right)=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$582$	11496	$$y^{\prime \prime \prime }+y^{\prime }x+ny=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$583$	11497	$$y^{\prime \prime \prime }-y^{\prime }x-ny=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$584$	11507	$$y^{\prime \prime \prime \prime }+4ax{y}^{\prime \prime \prime }+6a^2{x}^2{y}^{\prime \prime }+4a^3{x}^3{y}^{\prime }+a^4{x}^{4}y=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$585$	11510	$$x{y}^{\prime \prime \prime \prime }-(6x^2+1)y^{\prime \prime \prime }+12x^3{y}^{\prime \prime }-(9x^2-7)x^2{y}^{\prime }+2(x^2-3)x^{3}y=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$586$	11511	$$x^2{y}^{\prime \prime \prime \prime }-2({\nu }^2{x}^2+6)y^{\prime \prime }+{\nu }^2({\nu }^2{x}^2+4)y=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$587$	11512	$$x^2{y}^{\prime \prime \prime \prime }+2x{y}^{\prime \prime \prime }+ay-b{x}^2=0$$	[[_high_order, _linear, _nonhomogeneous]]	✓	✗
$588$	11515	$$x^2{y}^{\prime \prime \prime \prime }+6x{y}^{\prime \prime \prime }+6y^{\prime \prime }-{\lambda }^{2}y=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$589$	11517	$$x^2{y}^{\prime \prime \prime \prime }+8x{y}^{\prime \prime \prime }+12y^{\prime \prime }-{\lambda }^{2}y=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$590$	11518	$$x^2{y}^{\prime \prime \prime \prime }+(2n-2\nu +4)x{y}^{\prime \prime \prime }+(n-\nu +1)(n-\nu +2)y^{\prime \prime }-\frac{b^{4}y}{16}=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$591$	11519	$$x^3{y}^{\prime \prime \prime \prime }+2x^2{y}^{\prime \prime \prime }-x{y}^{\prime \prime }+y^{\prime }-a^4{x}^{3}y=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$592$	11521	$$x^4{y}^{\prime \prime \prime \prime }-2n(n+1)x^2{y}^{\prime \prime }+4n(n+1)x{y}^{\prime }+(a{x}^4+n(n+1)(n+3)(n-2))y=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$593$	11522	$$x^4{y}^{\prime \prime \prime \prime }+4x^3{y}^{\prime \prime \prime }-(4n^2-1)x^2{y}^{\prime \prime }+(4n^2-1)x{y}^{\prime }-4y{x}^4=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$594$	11523	$$x^4{y}^{\prime \prime \prime \prime }+4x^3{y}^{\prime \prime \prime }-(4n^2-1)x^2{y}^{\prime \prime }-(4n^2-1)x{y}^{\prime }+(-4x^4+4n^2-1)y=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$595$	11524	$$x^4{y}^{\prime \prime \prime \prime }+4x^3{y}^{\prime \prime \prime }-(4n^2+3)x^2{y}^{\prime \prime }+(12n^2-3)x{y}^{\prime }-(4x^4+12n^2-3)y=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$596$	11525	$$x^4{y}^{\prime \prime \prime \prime }+6x^3{y}^{\prime \prime \prime }+(4x^4+(-{\rho }^2-{\sigma }^2+7)x^2)y^{\prime \prime }+(16x^3+(-{\rho }^2-{\sigma }^2+1)x)y^{\prime }+({\rho }^2{\sigma }^2+8x^2)y=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$597$	11526	$$x^4{y}^{\prime \prime \prime \prime }+6x^3{y}^{\prime \prime \prime }+(4x^4+(-2{\mu }^2-2{\nu }^2+7)x^2)y^{\prime \prime }+(16x^3+(-2{\mu }^2-2{\nu }^2+1)x)y^{\prime }+(8x^2+{({\mu }^2-{\nu }^2)}^2)y=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$598$	11529	$$x^4{y}^{\prime \prime \prime \prime }+(6-4a)x^3{y}^{\prime \prime \prime }+(4b^2{c}^2{x}^{2c}+6{(a-1)}^2-2c^2({\mu }^2+{\nu }^2)+1)x^2{y}^{\prime \prime }+(4(3c-2a+1)b^2{c}^2{x}^{2c}+(2a-1)(2c^2({\mu }^2+{\nu }^2)-2a(a-1)-1))x{y}^{\prime }+(4(a-c)(a-2c)b^2{c}^2{x}^{2c}+(c\mu +c\nu +a)(c\mu +c\nu -a)(c\mu -c\nu +a)(c\mu -c\nu -a))y=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$599$	11530	$$x^4{y}^{\prime \prime \prime \prime }+(6-4a-4c)x^3{y}^{\prime \prime \prime }+(-2{\nu }^2{c}^2+2a^2+4{(a+c-1)}^2+4(a-1)(c-1)-1)x^2{y}^{\prime \prime }+(2{\nu }^2{c}^2-2a^2-(2a-1)(2c-1))(2a+2c-1)x{y}^{\prime }+((-{\nu }^2{c}^2+a^2)(-{\nu }^2{c}^2+a^2+4ac+4c^2)-b^4{c}^4{x}^{4c})y=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$600$	11531	$${\nu }^4{x}^4{y}^{\prime \prime \prime \prime }+(4\nu -2){\nu }^3{x}^3{y}^{\prime \prime \prime }+(\nu -1)(2\nu -1){\nu }^2{x}^2{y}^{\prime \prime }-\frac{b^4{x}^{\frac{2}{\nu }}y}{16}=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$601$	11532	$${(x^2-1)}^2{y}^{\prime \prime \prime \prime }+10x(x^2-1)y^{\prime \prime \prime }+(24x^2-8-2(\mu (\mu +1)+\nu (\nu +1))(x^2-1))y^{\prime \prime }-6x(\mu (\mu +1)+\nu (\nu +1)-2)y^{\prime }+({(\mu (\mu +1)-\nu (\nu +1))}^2-2\mu (\mu +1)-2\nu (\nu +1))y=0$$	[[_high_order, _with_linear_symmetries]]	✓	✗
$602$	11534	$$y^{\prime \prime \prime \prime }\sin {\left(x\right)}^4+2y^{\prime \prime \prime }\sin {\left(x\right)}^3\cos \left(x\right)+y^{\prime \prime }\sin {\left(x\right)}^2(\sin {\left(x\right)}^2-3)+y^{\prime }\sin \left(x\right)\cos \left(x\right)(2\sin {\left(x\right)}^2+3)+(a^4\sin {\left(x\right)}^4-3)y=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$603$	11535	$$y^{\prime \prime \prime \prime }\sin {\left(x\right)}^6+4y^{\prime \prime \prime }\sin {\left(x\right)}^5\cos \left(x\right)-6y^{\prime \prime }\sin {\left(x\right)}^6-4y^{\prime }\sin {\left(x\right)}^5\cos \left(x\right)+y\sin {\left(x\right)}^6-f=0$$	[[_high_order, _linear, _nonhomogeneous]]	✓	✓
$604$	11538	$$y^{\prime \prime \prime \prime }-2a^2{y}^{\prime \prime }+a^{4}y-\lambda (ax-b)(y^{\prime \prime }-a^{2}y)=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$605$	11544	$$x{y}^{\left(5\right)}-mn{y}^{\prime \prime \prime \prime }+yax=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$606$	11547	$$x^2{y}^{\prime \prime \prime \prime }-ay=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$607$	11548	$$x^{10}{y}^{\left(5\right)}-ay=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$608$	11549	$$x^{5/2}{y}^{\left(5\right)}-ay=0$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$609$	11563	$$y^{\prime \prime }-\frac{1}{{(a{y}^2+bxy+c{x}^2+\alpha y+\beta x+\gamma )}^{3/2}}=0$$	[NONE]	✓	✗
$610$	11570	$$y^{\prime \prime }=\frac{f\left(\frac{y}{\sqrt{x}}\right)}{x^{3/2}}$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$611$	11573	$$y^{\prime \prime }+5a{y}^{\prime }-6y^2+6a^{2}y=0$$	[[_2nd_order, _missing_x]]	✓	✓
$612$	11574	$$y^{\prime \prime }+3a{y}^{\prime }-2y^3+2a^{2}y=0$$	[[_2nd_order, _missing_x]]	✓	✓
$613$	11581	$$y^{\prime \prime }+y{y}^{\prime }-y^3+ay=0$$	[[_2nd_order, _missing_x]]	✓	✓
$614$	11582	$$y^{\prime \prime }+(y+3a)y^{\prime }-y^3+a{y}^2+2a^{2}y=0$$	[[_2nd_order, _missing_x]]	✓	✓
$615$	11584	$$y^{\prime \prime }+(3y+f\left(x\right))y^{\prime }+y^3+y^{2}f\left(x\right)=0$$	[[_2nd_order, _with_potential_symmetries]]	✓	✓
$616$	11585	$$y^{\prime \prime }-3y{y}^{\prime }-3a{y}^2-4a^{2}y-b=0$$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$617$	11586	$$y^{\prime \prime }-(3y+f\left(x\right))y^{\prime }+y^3+y^{2}f\left(x\right)=0$$	[[_2nd_order, _with_potential_symmetries]]	✓	✓
$618$	11595	$$y^{\prime \prime }-a{(y^{\prime }x-y)}^v=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$619$	11599	$$y^{\prime \prime }=a\sqrt{{y^{\prime }}^2+b{y}^2}$$	[[_2nd_order, _missing_x]]	✓	✓
$620$	11603	$$y^{\prime \prime }=2a(c+bx+y){(1+{y^{\prime }}^2)}^{3/2}$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]	✓	✓
$621$	11612	$$x{y}^{\prime \prime }-x^2{y^{\prime }}^2+2y^{\prime }+y^2=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$622$	11613	$$x{y}^{\prime \prime }+a{(y^{\prime }x-y)}^2-b=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$623$	11618	$$x^2{y}^{\prime \prime }+a{(y^{\prime }x-y)}^2-b{x}^2=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$624$	11620	$$x^2{y}^{\prime \prime }-\sqrt{a{x}^2{y^{\prime }}^2+b{y}^2}=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$625$	11623	$$9x^2{y}^{\prime \prime }+a{y}^3+2y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$626$	11625	$$x^3{y}^{\prime \prime }-a{(y^{\prime }x-y)}^2=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$627$	11629	$$x^4{y}^{\prime \prime }-x(x^2+2y)y^{\prime }+4y^2=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$628$	11630	$$x^4{y}^{\prime \prime }-x^2(x+y^{\prime })y^{\prime }+4y^2=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$629$	11631	$$x^4{y}^{\prime \prime }+{(y^{\prime }x-y)}^3=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$630$	11633	$${(a{x}^2+bx+c)}^{3/2}{y}^{\prime \prime }-F\left(\frac{y}{\sqrt{a{x}^2+bx+c}}\right)=0$$	[NONE]	✓	✓
$631$	11650	$$y{y}^{\prime \prime }-{y^{\prime }}^2+(\tan \left(x\right)+\cot \left(x\right))y{y}^{\prime }+(\cos {\left(x\right)}^2-n^2\cot {\left(x\right)}^2)y^2\ln \left(y\right)=0$$	[[_2nd_order, _reducible, _mu_xy]]	✓	✓
$632$	11651	$$y{y}^{\prime \prime }-{y^{\prime }}^2-f\left(x\right)y{y}^{\prime }-g\left(x\right)y^2=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$633$	11657	$$y{y}^{\prime \prime }+a{y^{\prime }}^2+by{y}^{\prime }+c{y}^2+d{y}^{1-a}=0$$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$634$	11660	$$y{y}^{\prime \prime }-{y^{\prime }}^2-1-2ay{(1+{y^{\prime }}^2)}^{3/2}=0$$	[[_2nd_order, _missing_x]]	✓	✓
$635$	11662	$$y^{\prime \prime }(x-y)+2y^{\prime }(y^{\prime }+1)=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]	✓	✓
$636$	11663	$$y^{\prime \prime }(x-y)-(y^{\prime }+1)(1+{y^{\prime }}^2)=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]	✓	✓
$637$	11664	$$y^{\prime \prime }(x-y)-h\left(y^{\prime }\right)=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]	✓	✓
$638$	11682	$$3y{y}^{\prime \prime }-2{y^{\prime }}^2-a{x}^2-bx-c=0$$	[NONE]	✓	✓
$639$	11694	$$xy{y}^{\prime \prime }+x{y^{\prime }}^2+ay{y}^{\prime }+f\left(x\right)=0$$	[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$640$	11698	$$xy{y}^{\prime \prime }-2x{y^{\prime }}^2+(1+y)y^{\prime }=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$641$	11701	$$xy{y}^{\prime \prime }+(\frac{ax}{\sqrt{b^2-x^2}}-x){y^{\prime }}^2-y{y}^{\prime }=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$642$	11704	$$x^2(-1+y)y^{\prime \prime }-2x^2{y^{\prime }}^2-2x(-1+y)y^{\prime }-2y{(-1+y)}^2=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$643$	11705	$$x^2(x+y)y^{\prime \prime }-{(y^{\prime }x-y)}^2=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$644$	11706	$$x^2(x-y)y^{\prime \prime }+a{(y^{\prime }x-y)}^2=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$645$	11707	$$2x^{2}y{y}^{\prime \prime }-x^2(1+{y^{\prime }}^2)+y^2=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$646$	11708	$$a{x}^{2}y{y}^{\prime \prime }+b{x}^2{y^{\prime }}^2+cxy{y}^{\prime }+d{y}^2=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$647$	11709	$$x{(x+1)}^{2}y{y}^{\prime \prime }-x{(x+1)}^2{y^{\prime }}^2+2{(x+1)}^{2}y{y}^{\prime }-a(x+2)y^2=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$648$	11710	$$8(-x^3+1)y{y}^{\prime \prime }-4(-x^3+1){y^{\prime }}^2-12x^{2}y{y}^{\prime }+3x{y}^2=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$649$	11712	$$y^2{y}^{\prime \prime }+y{y^{\prime }}^2+ax=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$650$	11713	$$y^2{y}^{\prime \prime }+y{y^{\prime }}^2-ax-b=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$651$	11716	$$(x+y^2)y^{\prime \prime }-2(x-y^2){y^{\prime }}^3+y^{\prime }(1+4y{y}^{\prime })=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]]	✓	✓
$652$	11717	$$(x^2+y^2)y^{\prime \prime }-(1+{y^{\prime }}^2)(y^{\prime }x-y)=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]	✓	✓
$653$	11718	$$(x^2+y^2)y^{\prime \prime }-2(1+{y^{\prime }}^2)(y^{\prime }x-y)=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]	✓	✓
$654$	11719	$$2y(1-y)y^{\prime \prime }-(1-2y){y^{\prime }}^2+y(1-y)y^{\prime }f\left(x\right)=0$$	[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$655$	11726	$$x{y}^2{y}^{\prime \prime }-a=0$$	[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]	✓	✓
$656$	11727	$$(a^2-x^2)(a^2-y^2)y^{\prime \prime }+(a^2-x^2)y{y^{\prime }}^2-x(a^2-y^2)y^{\prime }=0$$	[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$657$	11729	$$x^3{y}^2{y}^{\prime \prime }+(x+y){(y^{\prime }x-y)}^3=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$658$	11738	$${(c+2bx+a{x}^2+y^2)}^2{y}^{\prime \prime }+dy=0$$	[NONE]	✓	✓
$659$	11740	$$\sqrt{x^2+y^2}{y}^{\prime \prime }-a{(1+{y^{\prime }}^2)}^{3/2}=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$660$	11745	$$(y^{\prime }x-y)y^{\prime \prime }+4{y^{\prime }}^2=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$661$	11746	$$(y^{\prime }x-y)y^{\prime \prime }-{(1+{y^{\prime }}^2)}^2=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$662$	11747	$$a{x}^3{y}^{\prime }{y}^{\prime \prime }+b{y}^2=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$663$	11750	$$({y^{\prime }}^2+a(y^{\prime }x-y))y^{\prime \prime }-b=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$664$	11751	$$(a\sqrt{1+{y^{\prime }}^2}-y^{\prime }x)y^{\prime \prime }-{y^{\prime }}^2-1=0$$	[[_2nd_order, _missing_y]]	✓	✓
$665$	11752	$${y^{\prime \prime }}^2-ay-b=0$$	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓
$666$	11754	$$2(x^2+1){y^{\prime \prime }}^2-x{y}^{\prime \prime }(x+4y^{\prime })+2(x+y^{\prime })y^{\prime }-2y=0$$	[NONE]	✓	✓
$667$	11755	$$3x^2{y^{\prime \prime }}^2-2(3y^{\prime }x+y)y^{\prime \prime }+4{y^{\prime }}^2=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$668$	11756	$$x^2(2-9x){y^{\prime \prime }}^2-6x(1-6x)y^{\prime }{y}^{\prime \prime }+6y{y}^{\prime \prime }-36x{y^{\prime }}^2=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$669$	11767	$$x^2{y}^{\prime \prime \prime }+x(-1+y)y^{\prime \prime }+x{y^{\prime }}^2+(1-y)y^{\prime }=0$$	[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	✓	✓
$670$	11768	$$y{y}^{\prime \prime \prime }-y^{\prime }{y}^{\prime \prime }+y^3{y}^{\prime }=0$$	[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]	✓	✓
$671$	11769	$$4y^2{y}^{\prime \prime \prime }-18y{y}^{\prime }{y}^{\prime \prime }+15{y^{\prime }}^3=0$$	[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]	✓	✓
$672$	11770	$$9y^2{y}^{\prime \prime \prime }-45y{y}^{\prime }{y}^{\prime \prime }+40{y^{\prime }}^3=0$$	[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]]	✓	✓
$673$	11777	$$9{y^{\prime \prime }}^2{y}^{\left(5\right)}-45y^{\prime \prime }{y}^{\prime \prime \prime }{y}^{\prime \prime \prime \prime }+40y^{\prime \prime \prime }=0$$	[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]]	✓	✓
$674$	11932	$$y^{\prime }=y^2+an{x}^{n-1}-a^2{x}^{2n}$$	[_Riccati]	✓	✓
$675$	11933	$$y^{\prime }=a{y}^2+b{x}^{2n}+c{x}^{n-1}$$	[_Riccati]	✓	✓
$676$	11937	$$y^{\prime }=a{x}^n{y}^2+bm{x}^{m-1}-a{b}^2{x}^{n+2m}$$	[_Riccati]	✓	✓
$677$	11952	$$y^{\prime }=y^2+a{x}^{n}y+a{x}^{n-1}$$	[_Riccati]	✓	✓
$678$	11955	$$y^{\prime }=y^2+a{x}^{n}y-ab{x}^n-b^2$$	[_Riccati]	✓	✓
$679$	11957	$$y^{\prime }=a{x}^n{y}^2+b{x}^{m}y+bc{x}^m-a{c}^2{x}^n$$	[_Riccati]	✓	✓
$680$	11980	$$x^2{y}^{\prime }=c{x}^2{y}^2+(a{x}^n+b)xy+\alpha x^{2n}+\beta x^n+\gamma$$	[_rational, _Riccati]	✓	✓
$681$	11981	$$x^2{y}^{\prime }=(\alpha x^{2n}+\beta x^n+\gamma )y^2+(a{x}^n+b)xy+c{x}^2$$	[_rational, _Riccati]	✓	✓
$682$	11982	$$(x^2-1)y^{\prime }+\lambda (1-2xy+y^2)=0$$	[_rational, _Riccati]	✓	✓
$683$	11984	$$(a{x}^2+b)y^{\prime }+\alpha y^2+\beta xy+\gamma =0$$	[_rational, _Riccati]	✓	✓
$684$	11987	$$(a{x}^2+bx+c)y^{\prime }=y^2+(ax+\mu )y-{\lambda }^2{x}^2+\lambda (b-\mu )x+\lambda c$$	[_rational, _Riccati]	✓	✓
$685$	11988	$$(a_2{x}^2+b_{2}x+c_2)y^{\prime }=y^2+(a_{1}x+b_1)y-\lambda (\lambda +a_1-a_2)x^2+\lambda (b_2-b_1)x+\lambda c_2$$	[_rational, _Riccati]	✓	✓
$686$	11989	$$(a_2{x}^2+b_{2}x+c_2)y^{\prime }=y^2+(a_{1}x+b_1)y+a_0{x}^2+b_{0}x+c_0$$	[_rational, _Riccati]	✓	✗
$687$	11993	$$x^3{y}^{\prime }=a{x}^3{y}^2+x(bx+c)y+\alpha x+\beta$$	[_rational, _Riccati]	✓	✓
$688$	12004	$$(a{x}^n+b{x}^m+c)y^{\prime }=\alpha x^k{y}^2+\beta x^{s}y-\alpha {\lambda }^2{x}^k+\beta \lambda x^s$$	[_rational, _Riccati]	✓	✓
$689$	12011	$$y^{\prime }=y^2+a{\mathrm{e}}^{\lambda x}y-ab{\mathrm{e}}^{\lambda x}-b^2$$	[_Riccati]	✓	✓
$690$	12020	$$y^{\prime }=a{\mathrm{e}}^{\mu x}{y}^2+ab{\mathrm{e}}^{(\lambda +\mu )x}y-b\lambda {\mathrm{e}}^{\lambda x}$$	[_Riccati]	✓	✓
$691$	12025	$$(a{\mathrm{e}}^{\lambda x}+b{\mathrm{e}}^{\mu x}+c)y^{\prime }=y^2+k{\mathrm{e}}^{\nu x}y-m^2+km{\mathrm{e}}^{\nu x}$$	[_Riccati]	✓	✓
$692$	12030	$$y^{\prime }={\mathrm{e}}^{\lambda x}{y}^2+a{x}^{n}y+a\lambda x^n{\mathrm{e}}^{-\lambda x}$$	[_Riccati]	✓	✓
$693$	12041	$$y^{\prime }x=a{x}^{2n}{\mathrm{e}}^{\lambda x}{y}^2+(b{x}^n{\mathrm{e}}^{\lambda x}-n)y+c{\mathrm{e}}^{\lambda x}$$	[_Riccati]	✓	✓
$694$	12051	$$(a\sinh \left(\lambda x\right)+b)y^{\prime }=y^2+c\sinh \left(\mu x\right)y-d^2+cd\sinh \left(\mu x\right)$$	[_Riccati]	✓	✓
$695$	12060	$$y^{\prime }=a\cosh \left(\lambda x\right)y^2+b\cosh \left(\lambda x\right)\sinh {\left(\lambda x\right)}^n$$	[_Riccati]	✓	✓
$696$	12061	$$(a\cosh \left(\lambda x\right)+b)y^{\prime }=y^2+c\cosh \left(\mu x\right)y-d^2+cd\cosh \left(\mu x\right)$$	[_Riccati]	✓	✓
$697$	12063	$$y^{\prime }=y^2+a\lambda -a(a+\lambda )\tanh {\left(\lambda x\right)}^2$$	[_Riccati]	✓	✓
$698$	12064	$$y^{\prime }=y^2+3a\lambda -{\lambda }^2-a(a+\lambda )\tanh {\left(\lambda x\right)}^2$$	[_Riccati]	✓	✓
$699$	12066	$$(a\tanh \left(\lambda x\right)+b)y^{\prime }=y^2+c\tanh \left(\mu x\right)y-d^2+cd\tanh \left(\mu x\right)$$	[_Riccati]	✓	✓
$700$	12067	$$y^{\prime }=y^2+a\lambda -a(a+\lambda )\coth {\left(\lambda x\right)}^2$$	[_Riccati]	✓	✓
$701$	12068	$$y^{\prime }=y^2-{\lambda }^2+3a\lambda -a(a+\lambda )\coth {\left(\lambda x\right)}^2$$	[_Riccati]	✓	✓
$702$	12070	$$(a\coth \left(\lambda x\right)+b)y^{\prime }=y^2+c\coth \left(\mu x\right)y-d^2+cd\coth \left(\mu x\right)$$	[_Riccati]	✓	✓
$703$	12088	$$y^{\prime }=a\ln {\left(x\right)}^n{y}^2+b\ln {\left(x\right)}^{m}y+bc\ln {\left(x\right)}^m-a{c}^2\ln {\left(x\right)}^n$$	[_Riccati]	✓	✓
$704$	12094	$$(a\ln \left(x\right)+b)y^{\prime }=y^2+c\ln {\left(x\right)}^{n}y-{\lambda }^2+\lambda c\ln {\left(x\right)}^n$$	[_Riccati]	✓	✓
$705$	12095	$$(a\ln \left(x\right)+b)y^{\prime }=\ln {\left(x\right)}^n{y}^2+cy-{\lambda }^2\ln {\left(x\right)}^n+\lambda c$$	[_Riccati]	✓	✓
$706$	12107	$$(a\sin \left(\lambda x\right)+b)y^{\prime }=y^2+c\sin \left(\mu x\right)y-d^2+cd\sin \left(\mu x\right)$$	[_Riccati]	✓	✓
$707$	12120	$$(a\cos \left(\lambda x\right)+b)y^{\prime }=y^2+c\cos \left(\mu x\right)y-d^2+cd\cos \left(\mu x\right)$$	[_Riccati]	✓	✓
$708$	12122	$$y^{\prime }=y^2+a\lambda +a(\lambda -a)\tan {\left(\lambda x\right)}^2$$	[_Riccati]	✓	✓
$709$	12123	$$y^{\prime }=y^2+{\lambda }^2+3a\lambda +a(\lambda -a)\tan {\left(\lambda x\right)}^2$$	[_Riccati]	✓	✓
$710$	12132	$$(a\tan \left(\lambda x\right)+b)y^{\prime }=y^2+k\tan \left(\mu x\right)y-d^2+kd\tan \left(\mu x\right)$$	[_Riccati]	✓	✓
$711$	12133	$$y^{\prime }=y^2+a\lambda +a(\lambda -a)\cot {\left(\lambda x\right)}^2$$	[_Riccati]	✓	✗
$712$	12134	$$y^{\prime }=y^2+{\lambda }^2+3a\lambda +a(\lambda -a)\cot {\left(\lambda x\right)}^2$$	[_Riccati]	✓	✓
$713$	12135	$$y^{\prime }=y^2-2ab\cot \left(ax\right)y+b^2-a^2$$	[_Riccati]	✓	✗
$714$	12139	$$y^{\prime }=a\cot {(\lambda x+\mu )}^k{(y-b{x}^n-c)}^2+bn{x}^{n-1}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	✓
$715$	12141	$$(a\cot \left(\lambda x\right)+b)y^{\prime }=y^2+c\cot \left(\mu x\right)y-d^2+cd\cot \left(\mu x\right)$$	[_Riccati]	✓	✓
$716$	12147	$$\sin {\left(2x\right)}^{n+1}{y}^{\prime }=a{y}^2\sin {\left(x\right)}^{2n}+b\cos {\left(x\right)}^{2n}$$	[_Riccati]	✓	✓
$717$	12158	$$y^{\prime }=\lambda \arcsin {\left(x\right)}^n{y}^2+ay+ab-b^2\lambda \arcsin {\left(x\right)}^n$$	[_Riccati]	✓	✓
$718$	12161	$$y^{\prime }=\lambda \arcsin {\left(x\right)}^n{(y-a{x}^m-b)}^2+am{x}^{m-1}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	✓
$719$	12164	$$y^{\prime }=y^2+\lambda \arccos {\left(x\right)}^{n}y-a^2+a\lambda \arccos {\left(x\right)}^n$$	[_Riccati]	✓	✓
$720$	12167	$$y^{\prime }=\lambda \arccos {\left(x\right)}^n{y}^2+ay+ab-b^2\lambda \arccos {\left(x\right)}^n$$	[_Riccati]	✓	✓
$721$	12170	$$y^{\prime }=\lambda \arccos {\left(x\right)}^n{(y-a{x}^m-b)}^2+am{x}^{m-1}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	✓
$722$	12176	$$y^{\prime }=\lambda \arctan {\left(x\right)}^n{y}^2+ay+ab-b^2\lambda \arctan {\left(x\right)}^n$$	[_Riccati]	✓	✓
$723$	12179	$$y^{\prime }=\lambda \arctan {\left(x\right)}^n{(y-a{x}^m-b)}^2+am{x}^{m-1}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	✓
$724$	12185	$$y^{\prime }=\lambda \mathrm{arccot}{\left(x\right)}^n{y}^2+ay+ab-b^2\lambda \mathrm{arccot}{\left(x\right)}^n$$	[_Riccati]	✓	✓
$725$	12188	$$y^{\prime }=\lambda \mathrm{arccot}{\left(x\right)}^n{(y-a{x}^m-b)}^2+am{x}^{m-1}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	✓
$726$	12198	$$y^{\prime }x=x^{2n}f\left(x\right)y^2+(a{x}^{n}f\left(x\right)-n)y+bf\left(x\right)$$	[_Riccati]	✓	✓
$727$	12216	$$y^{\prime }x=f\left(x\right){(y+a\ln \left(x\right))}^2-a$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]	✓	✓
$728$	12228	$$y^{\prime }=\frac{y^2{f}^{\prime }\left(x\right)}{g\left(x\right)}-\frac{g^{\prime }\left(x\right)}{f\left(x\right)}$$	[_Riccati]	✓	✓
$729$	12249	$$y{y}^{\prime }-y=-\frac{2x}{9}+A+\frac{B}{\sqrt{x}}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$730$	12250	$$y{y}^{\prime }-y=2A(\sqrt{x}+4A+\frac{3A^2}{\sqrt{x}})$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$731$	12251	$$y{y}^{\prime }-y=Ax+\frac{B}{x}-\frac{B^2}{x^3}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$732$	12253	$$y{y}^{\prime }-y=\frac{A}{x}-\frac{A^2}{x^3}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$733$	12254	$$y{y}^{\prime }-y=A+B{\mathrm{e}}^{-\frac{2x}{A}}$$	[[_Abel, ‘2nd type‘, ‘class A‘]]	✓	✗
$734$	12255	$$y{y}^{\prime }-y=A({\mathrm{e}}^{\frac{2x}{A}}-1)$$	[[_Abel, ‘2nd type‘, ‘class A‘]]	✓	✗
$735$	12257	$$y{y}^{\prime }-y=-\frac{2x}{9}+6A^2(1+\frac{2A}{\sqrt{x}})$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$736$	12259	$$y{y}^{\prime }-y=\frac{(2m+1)x}{4m^2}+\frac{A}{x}-\frac{A^2}{x^3}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$737$	12260	$$y{y}^{\prime }-y=\frac{4}{9}x+2A{x}^2+2A^2{x}^3$$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓
$738$	12262	$$y{y}^{\prime }-y=\frac{A}{x}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$739$	12263	$$y{y}^{\prime }-y=-\frac{x}{4}+\frac{A(\sqrt{x}+5A+\frac{3A^2}{\sqrt{x}})}{4}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$740$	12264	$$y{y}^{\prime }-y=\frac{2a^2}{\sqrt{8a^2+x^2}}$$	[[_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$741$	12265	$$y{y}^{\prime }-y=2x+\frac{A}{x^2}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$742$	12268	$$y{y}^{\prime }-y=-\frac{4x}{25}+\frac{A}{\sqrt{x}}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$743$	12269	$$y{y}^{\prime }-y=-\frac{9x}{100}+\frac{A}{x^{5/3}}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$744$	12270	$$y{y}^{\prime }-y=-\frac{12x}{49}+\frac{2A(5\sqrt{x}+34A+\frac{15A^2}{\sqrt{x}})}{49}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$745$	12271	$$y{y}^{\prime }-y=-\frac{12x}{49}+\frac{A(25\sqrt{x}+41A+\frac{10A^2}{\sqrt{x}})}{98}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$746$	12272	$$y{y}^{\prime }-y=-\frac{2x}{9}+\frac{A}{\sqrt{x}}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$747$	12278	$$y{y}^{\prime }-y=\frac{A}{\sqrt{x}}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$748$	12279	$$y{y}^{\prime }-y=\frac{A}{x^2}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$749$	12280	$$y{y}^{\prime }-y=A(n+2)(\sqrt{x}+2(n+2)A+\frac{(n+1)(n+3)A^2}{\sqrt{x}})$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$750$	12281	$$y{y}^{\prime }-y=A(n+2)(\sqrt{x}+2(n+2)A+\frac{(2n+3)A^2}{\sqrt{x}})$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$751$	12282	$$y{y}^{\prime }-y=A\sqrt{x}+2A^2+\frac{B}{\sqrt{x}}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$752$	12283	$$y{y}^{\prime }-y=2A^2-A\sqrt{x}$$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✗
$753$	12286	$$y{y}^{\prime }-y=-\frac{3x}{16}+\frac{3A}{x^{1/3}}-\frac{12A^2}{x^{5/3}}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$754$	12290	$$y{y}^{\prime }-y=A{x}^2-\frac{9}{625A}$$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓
$755$	12291	$$y{y}^{\prime }-y=-\frac{6}{25}x-A{x}^2$$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓
$756$	12292	$$y{y}^{\prime }-y=\frac{6}{25}x-A{x}^2$$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓
$757$	12293	$$y{y}^{\prime }-y=12x+\frac{A}{x^{5/2}}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$758$	12295	$$y{y}^{\prime }-y=2x+2A(10\sqrt{x}+31A+\frac{30A^2}{\sqrt{x}})$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$759$	12298	$$y{y}^{\prime }-y=-\frac{12x}{49}+\frac{A(5\sqrt{x}+262A+\frac{65A^2}{\sqrt{x}})}{49}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$760$	12299	$$y{y}^{\prime }-y=-\frac{12x}{49}+A\sqrt{x}$$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✗
$761$	12300	$$y{y}^{\prime }-y=6x+\frac{A}{x^4}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$762$	12303	$$y{y}^{\prime }-y=-\frac{10x}{49}+\frac{2A(4\sqrt{x}+61A+\frac{12A^2}{\sqrt{x}})}{49}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$763$	12304	$$y{y}^{\prime }-y=-\frac{12x}{49}+\frac{2A(\sqrt{x}+166A+\frac{55A^2}{\sqrt{x}})}{49}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$764$	12311	$$y{y}^{\prime }-y=-\frac{6x}{25}+\frac{4B^2((2-A)x^{1/3}-\frac{3B(2A+1)}{2}+\frac{B^2(1-3A)}{x^{1/3}}-\frac{A{B}^3}{x^{2/3}})}{75}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$765$	12323	$$y{y}^{\prime }=(ax+b)y+1$$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓
$766$	12324	$$y{y}^{\prime }=\frac{y}{{(ax+b)}^2}+1$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$767$	12325	$$y{y}^{\prime }=(a-\frac{1}{ax})y+1$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$768$	12327	$$y{y}^{\prime }=\frac{3y}{\sqrt{a{x}^{3/2}+8x}}+1$$	[[_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$769$	12328	$$y{y}^{\prime }=(\frac{a}{x^{2/3}}-\frac{2}{3a{x}^{1/3}})y+1$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$770$	12329	$$y{y}^{\prime }=a{\mathrm{e}}^{\lambda x}y+1$$	[[_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓
$771$	12335	$$y{y}^{\prime }=(ax+3b)y+c{x}^3-ab{x}^2-2b^{2}x$$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✗
$772$	12337	$$2y{y}^{\prime }=(7ax+5b)y-3a^2{x}^3-2c{x}^2-3b^{2}x$$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✗
$773$	12339	$$y{y}^{\prime }+x(a{x}^2+b)y+x=0$$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓
$774$	12340	$$y{y}^{\prime }+a(1-\frac{1}{x})y=a^2$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$775$	12341	$$y{y}^{\prime }-a(1-\frac{b}{x})y=a^{2}b$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$776$	12342	$$y{y}^{\prime }=x^{n-1}((2n+1)x+an)y-n{x}^{2n}(x+a)$$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✗
$777$	12343	$$y{y}^{\prime }=a(-nb+x)x^{n-1}y+c(x^2-(2n+1)bx+n(n+1)b^2)x^{2n-1}$$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓
$778$	12349	$$y{y}^{\prime }-\frac{a((m-1)x+1)y}{x}=\frac{a^2(mx+1)(x-1)}{x}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$779$	12350	$$y{y}^{\prime }-a(1-\frac{b}{\sqrt{x}})y=\frac{a^{2}b}{\sqrt{x}}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$780$	12351	$$y{y}^{\prime }=\frac{3y}{{(ax+b)}^{1/3}{x}^{5/3}}+\frac{3}{{(ax+b)}^{2/3}{x}^{7/3}}$$	[[_Abel, ‘2nd type‘, ‘class B‘]]	✓	✓
$781$	12353	$$y{y}^{\prime }+\frac{a(6x-1)y}{2x}=-\frac{a^2(x-1)(4x-1)}{2x}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$782$	12362	$$y{y}^{\prime }+\frac{a(7x-12)y}{10x^{7/5}}=-\frac{a^2(x-1)(x-16)}{10x^{9/5}}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$783$	12365	$$y{y}^{\prime }-\frac{a(x+1)y}{2x^{7/4}}=\frac{a^2(x-1)(3x+5)}{4x^{5/2}}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$784$	12370	$$y{y}^{\prime }-\frac{a(5x-4)y}{x^4}=\frac{a^2(x-1)(3x-1)}{x^7}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$785$	12373	$$y{y}^{\prime }+\frac{a(x-2)y}{x}=\frac{2a^2(x-1)}{x}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$786$	12377	$$y{y}^{\prime }+\frac{a(33x+2)y}{30x^{6/5}}=-\frac{a^2(x-1)(9x-4)}{30x^{7/5}}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$787$	12385	$$y{y}^{\prime }-\frac{a(x+4)y}{5x^{8/5}}=\frac{a^2(x-1)(3x+7)}{5x^{11/5}}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$788$	12386	$$y{y}^{\prime }-\frac{a(2x-1)y}{x^{5/2}}=\frac{a^2(x-1)(3x+1)}{2x^4}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$789$	12387	$$y{y}^{\prime }+\frac{a(x-6)y}{5x^{7/5}}=\frac{2a^2(x-1)(x+4)}{5x^{9/5}}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$790$	12390	$$y{y}^{\prime }-\frac{a((k+1)x-1)y}{x^2}=\frac{a^2(k+1)(x-1)}{x^2}$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$791$	12393	$$y{y}^{\prime }-((2n-1)x-an)x^{-n-1}y=n(x-a)x^{-2n}$$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✗
$792$	12400	$$y{y}^{\prime }-a(\frac{n+2}{n}+b{x}^n)y=-\frac{a^{2}x(\frac{n+1}{n}+b{x}^n)}{n}$$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✗
$793$	12401	$$y{y}^{\prime }=(a{\mathrm{e}}^x+b)y+c{\mathrm{e}}^{2x}-ab{\mathrm{e}}^x-b^2$$	[[_Abel, ‘2nd type‘, ‘class A‘]]	✓	✗
$794$	12403	$$y{y}^{\prime }=(a{\mathrm{e}}^{\lambda x}+b)y+c(a^2{\mathrm{e}}^{2\lambda x}+ab(\lambda x+1){\mathrm{e}}^{\lambda x}+b^2\lambda x)$$	[[_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓
$795$	12404	$$y{y}^{\prime }={\mathrm{e}}^{\lambda x}(2a\lambda x+a+b)y-{\mathrm{e}}^{2\lambda x}(a^2\lambda x^2+abx+c)$$	[[_Abel, ‘2nd type‘, ‘class A‘]]	✓	✗
$796$	12406	$$y{y}^{\prime }+a(2bx+1){\mathrm{e}}^{bx}y=-a^{2}b{x}^2{\mathrm{e}}^{2bx}$$	[[_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓
$797$	12407	$$y{y}^{\prime }-a(1+2n+2n(n+1)x){\mathrm{e}}^{(n+1)x}y=-a^{2}n(n+1)(nx+1)x{\mathrm{e}}^{2(n+1)x}$$	[[_Abel, ‘2nd type‘, ‘class A‘]]	✓	✗
$798$	12408	$$y{y}^{\prime }+a(1+2b\sqrt{x}){\mathrm{e}}^{2b\sqrt{x}}y=-a^{2}b{x}^{3/2}{\mathrm{e}}^{4b\sqrt{x}}$$	[[_Abel, ‘2nd type‘, ‘class A‘]]	✓	✗
$799$	12411	$$y{y}^{\prime }=(2\ln \left(x\right)+a+1)y+x(-\ln {\left(x\right)}^2-a\ln \left(x\right)+b)$$	[[_Abel, ‘2nd type‘, ‘class A‘]]	✓	✗
$800$	12421	$$x{y}^{\prime }y=-n{y}^2+a(2n+1)xy+by-a^{2}n{x}^2-abx+c$$	[_rational, [_Abel, ‘2nd type‘, ‘class B‘]]	✓	✗
$801$	12425	$$y^{\prime \prime }-(a{x}^2+b)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$802$	12427	$$y^{\prime \prime }-(a{x}^2+bxc)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$803$	12429	$$y^{\prime \prime }-a(a{x}^{2n}+n{x}^{n-1})y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$804$	12430	$$y^{\prime \prime }-a{x}^{n-2}(a{x}^n+n+1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$805$	12431	$$y^{\prime \prime }+(a{x}^{2n}+b{x}^{n-1})y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$806$	12434	$$y^{\prime \prime }+a{y}^{\prime }-(b{x}^2+c)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$807$	12437	$$y^{\prime \prime }+a{y}^{\prime }+b(-b{x}^{2n}+a{x}^n+n{x}^{n-1})y=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✗
$808$	12438	$$y^{\prime \prime }+a{y}^{\prime }+b(-b{x}^{2n}-a{x}^n+n{x}^{n-1})y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$809$	12439	$$y^{\prime \prime }+y^{\prime }x+(n-1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$810$	12440	$$y^{\prime \prime }-2y^{\prime }x+2ny=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$811$	12441	$$y^{\prime \prime }+ax{y}^{\prime }+by=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$812$	12442	$$y^{\prime \prime }+ax{y}^{\prime }+bxy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$813$	12443	$$y^{\prime \prime }+ax{y}^{\prime }+(bx+c)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$814$	12444	$$y^{\prime \prime }+2ax{y}^{\prime }+(b{x}^4+a^2{x}^2+cx+a)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$815$	12449	$$y^{\prime \prime }+(ax+b)y^{\prime }+(cx+d)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$816$	12450	$$y^{\prime \prime }+(ax+b)y^{\prime }+c((a-c)x^2+bx+1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$817$	12452	$$y^{\prime \prime }+(ax+b)y^{\prime }+(\alpha x^2+\beta x+\gamma )y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$818$	12458	$$y^{\prime \prime }+(a{x}^2+bx)y^{\prime }+(\alpha x^2+\beta x+\gamma )y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$819$	12466	$$y^{\prime \prime }+a{x}^n{y}^{\prime }+b{x}^{n-1}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$820$	12468	$$y^{\prime \prime }+a{x}^n{y}^{\prime }+(b{x}^{2n}+c{x}^{n-1})y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$821$	12470	$$y^{\prime \prime }+2a{x}^n{y}^{\prime }+(a^2{x}^{2n}+b{x}^{2m}+an{x}^{n-1}+c{x}^{m-1})y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$822$	12472	$$y^{\prime \prime }+(a{x}^n+2b)y^{\prime }+(ab{x}^n-a{x}^{n-1}+b^2)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$823$	12475	$$y^{\prime \prime }+x^n(a{x}^2+(ac+b)x+bc)y^{\prime }-x^n(ax+b)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$824$	12476	$$y^{\prime \prime }+(a{x}^n+b{x}^m)y^{\prime }-(a{x}^{n-1}+b{x}^{m-1})y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$825$	12478	$$y^{\prime \prime }+(a{x}^n+b{x}^m)y^{\prime }+(a(n+1)x^{n-1}+b(m+1)x^{m-1})y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$826$	12485	$$x{y}^{\prime \prime }+a{y}^{\prime }+(bx+c)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$827$	12487	$$x{y}^{\prime \prime }+(1-3n)y^{\prime }-a^2{n}^2{x}^{2n-1}y=0$$	[[_Emden, _Fowler]]	✓	✓
$828$	12489	$$x{y}^{\prime \prime }+a{y}^{\prime }+b{x}^n(-b{x}^{n+1}+a+n)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$829$	12491	$$x{y}^{\prime \prime }+(b-x)y^{\prime }-ay=0$$	[_Laguerre]	✓	✓
$830$	12492	$$x{y}^{\prime \prime }+(ax+b)y^{\prime }+c((a-c)x+b)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$831$	12494	$$x{y}^{\prime \prime }+((a+b)x+m+n)y^{\prime }+(abx+an+bm)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$832$	12495	$$x{y}^{\prime \prime }+(ax+b)y^{\prime }+(cx+d)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$833$	12499	$$x{y}^{\prime \prime }-(2ax+1)y^{\prime }+b{x}^{3}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$834$	12500	$$x{y}^{\prime \prime }+(ab{x}^2+b-5)y^{\prime }+2a^2(b-2)x^{3}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$835$	12504	$$x{y}^{\prime \prime }+(a{x}^2+bx+c)y^{\prime }+(c-1)(ax+b)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$836$	12505	$$x{y}^{\prime \prime }+(a{x}^2+bx+c)y^{\prime }+(A{x}^2+Bx+\mathrm{C}0)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$837$	12506	$$x{y}^{\prime \prime }+(a{x}^2+bx+2)y^{\prime }+(c{x}^2+dx+b)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$838$	12507	$$x{y}^{\prime \prime }+(a{x}^3+b)y^{\prime }+a(b-1)x^{2}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$839$	12511	$$x{y}^{\prime \prime }+(a{x}^3+b{x}^2+cx+d)y^{\prime }+(d-1)(a{x}^2+bx+c)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$840$	12513	$$x{y}^{\prime \prime }+(a{x}^n+2)y^{\prime }+a{x}^{n-1}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$841$	12514	$$x{y}^{\prime \prime }+(x^n+1-n)y^{\prime }+b{x}^{2n-1}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$842$	12516	$$x{y}^{\prime \prime }+(a{x}^n+b)y^{\prime }+a(b-1)x^{n-1}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$843$	12517	$$x{y}^{\prime \prime }+(a{x}^n+b)y^{\prime }+a(b+n-1)x^{n-1}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$844$	12520	$$x{y}^{\prime \prime }+(a{x}^n+b)y^{\prime }+(c{x}^{2n-1}+d{x}^{n-1})y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$845$	12521	$$x{y}^{\prime \prime }+(a{x}^n+b{x}^{n-1}+2)y^{\prime }+b{x}^{n-2}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$846$	12527	$$(a_{1}x+a_0)y^{\prime \prime }+(b_{1}x+b_0)y^{\prime }-m{b}_{1}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$847$	12528	$$(ax+b)y^{\prime \prime }+s(cx+d)y^{\prime }-s^2((a+c)x+b+d)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$848$	12529	$$(a_{2}x+b_2)y^{\prime \prime }+(a_{1}x+b_1)y^{\prime }+(a_{0}x+b_0)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$849$	12535	$$x^2{y}^{\prime \prime }-(a^2{x}^2+2abx+b^2-b)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$850$	12536	$$x^2{y}^{\prime \prime }+(a{x}^2+bx+c)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$851$	12538	$$x^2{y}^{\prime \prime }-(a^2{x}^4+a(2b-1)x^2+b(b+1))y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$852$	12540	$$x^2{y}^{\prime \prime }-(a^2{x}^{2n}+a(2b+n-1)x^n+b(b-1))y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$853$	12541	$$x^2{y}^{\prime \prime }+(a{x}^{2n}+b{x}^n+c)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$854$	12542	$$x^2{y}^{\prime \prime }+(a{x}^{3n}+b{x}^{2n}+\frac{1}{4}-\frac{n^2}{4})y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$855$	12552	$$x^2{y}^{\prime \prime }+\lambda x{y}^{\prime }+(a{x}^2+bx+c)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$856$	12554	$$x^2{y}^{\prime \prime }+ax{y}^{\prime }+x^n(b{x}^n+c)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$857$	12555	$$x^2{y}^{\prime \prime }+(ax+b)y^{\prime }+cy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$858$	12556	$$x^2{y}^{\prime \prime }+a{x}^2{y}^{\prime }+(b{x}^2+cx+d)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$859$	12557	$$x^2{y}^{\prime \prime }+(a{x}^2+b)y^{\prime }+c((a-c)x^2+b)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$860$	12559	$$x^2{y}^{\prime \prime }+(a{x}^2+bx)y^{\prime }+(k(a-k)x^2+(an+bk-2kn)x+n(b-n-1))y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$861$	12560	$$a_2{x}^2{y}^{\prime \prime }+(a_1{x}^2+b_{1}x)y^{\prime }+(a_0{x}^2+b_{0}x+c_0)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$862$	12562	$$x^2{y}^{\prime \prime }-2x(x^2-a)y^{\prime }+(2n{x}^2+({(-1)}^n-1)a)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$863$	12563	$$x^2{y}^{\prime \prime }+x(a{x}^2+bx+c)y^{\prime }+(A{x}^3+B{x}^2+Cx+d)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$864$	12566	$$x^2{y}^{\prime \prime }+(a{x}^n+b)y^{\prime }x+b(a{x}^n-1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$865$	12567	$$x^2{y}^{\prime \prime }+(a{x}^n+b)y^{\prime }x+(\alpha x^{2n}+\beta x^n+\gamma )y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$866$	12568	$$x^2{y}^{\prime \prime }+x(2a{x}^n+b)y^{\prime }+(a^2{x}^{2n}+a(b+n-1)x^n+\alpha x^{2m}+\beta x^m+\gamma )y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$867$	12570	$$(-x^2+1)y^{\prime \prime }+n(n-1)y=0$$	[_Gegenbauer]	✓	✓
$868$	12571	$$(-a^2+x^2)y^{\prime \prime }+b{y}^{\prime }-6y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$869$	12574	$$(-x^2+1)y^{\prime \prime }-2y^{\prime }x+n(n+1)y=0$$	[_Gegenbauer]	✓	✓
$870$	12575	$$(-x^2+1)y^{\prime \prime }-2y^{\prime }x+\nu (\nu +1)y=0$$	[_Gegenbauer]	✓	✓
$871$	12577	$$(x^2-1)y^{\prime \prime }+2(n+1)x{y}^{\prime }-(\nu +n+1)(\nu -n)y=0$$	[_Gegenbauer]	✓	✓
$872$	12578	$$(x^2-1)y^{\prime \prime }-2(n-1)x{y}^{\prime }-(\nu -n+1)(\nu +n)y=0$$	[_Gegenbauer]	✓	✓
$873$	12579	$$(x^2-1)y^{\prime \prime }+(2a+1)y^{\prime }-b(2a+b)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$874$	12580	$$(-x^2+1)y^{\prime \prime }+(2a-3)x{y}^{\prime }+(n+1)(n+2a-1)y=0$$	[_Gegenbauer]	✓	✓
$875$	12581	$$(-x^2+1)y^{\prime \prime }+(\beta -\alpha -(\alpha +\beta +2)x)y^{\prime }+n(n+\alpha +\beta +1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$876$	12582	$$(-x^2+1)y^{\prime \prime }+(\alpha -\beta +(\alpha +\beta -2)x)y^{\prime }+(n+1)(n+\alpha +\beta )y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$877$	12587	$$(a{x}^2+b)y^{\prime \prime }+(2n+1)ax{y}^{\prime }+cy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$878$	12588	$$(-x^2+1)y^{\prime \prime }-y^{\prime }x+(2a{x}^2+b)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$879$	12589	$$(-x^2+1)y^{\prime \prime }+(ax+b)y^{\prime }+cy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$880$	12590	$$(a{x}^2+b)y^{\prime \prime }+(c{x}^2+d)y^{\prime }+\lambda ((-a\lambda +c)x^2+d-b\lambda )y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$881$	12591	$$(a{x}^2+b)y^{\prime \prime }+(\lambda (a+c)x^2+(c-a)x+2b\lambda )y^{\prime }+{\lambda }^2(c{x}^2+b)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$882$	12592	$$x(x-1)y^{\prime \prime }+((\alpha +\beta +1)x-\gamma )y^{\prime }+\alpha \beta y=0$$	[_Jacobi]	✓	✓
$883$	12593	$$x(x+a)y^{\prime \prime }+(bx+c)y^{\prime }+dy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$884$	12594	$$2x(x-1)y^{\prime \prime }+(2x-1)y^{\prime }+(ax+b)y=0$$	[_Jacobi]	✓	✓
$885$	12597	$$(a{x}^2+bx+c)y^{\prime \prime }+(kx+d)y^{\prime }-ky=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$886$	12600	$$(a_2{x}^2+b_{2}x+c_2)y^{\prime \prime }+(b_{1}x+c_1)y^{\prime }+c_{0}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$887$	12601	$$(a{x}^2+bx+c)y^{\prime \prime }-(-k^2+x^2)y^{\prime }+(x+k)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$888$	12602	$$(a{x}^2+bx+c)y^{\prime \prime }+(k^3+x^3)y^{\prime }-(k^2-kx+x^2)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$889$	12604	$$x^3{y}^{\prime \prime }+(a{x}^2+b)y^{\prime }+cxy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$890$	12605	$$x^3{y}^{\prime \prime }+(a{x}^2+bx)y^{\prime }+by=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$891$	12606	$$x^3{y}^{\prime \prime }+(a{x}^2+bx)y^{\prime }+cy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$892$	12607	$$x^3{y}^{\prime \prime }+(a{x}^2+bx)y^{\prime }+(cx+d)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$893$	12608	$$x^3{y}^{\prime \prime }+(a{x}^3+abx-x^2+b)y^{\prime }+a^{2}bxy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$894$	12611	$$x(x^2+a)y^{\prime \prime }+(b{x}^2+c)y^{\prime }+sxy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$895$	12612	$$x^2(ax+b)y^{\prime \prime }+(c{x}^2+(a\lambda +2b)x+b\lambda )y^{\prime }+\lambda (c-2a)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$896$	12615	$$x^2(x+a_2)y^{\prime \prime }+x(b_{1}x+a_1)y^{\prime }+(b_{0}x+a_0)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$897$	12616	$$(a{x}^3+b{x}^2+cx)y^{\prime \prime }+(\alpha x^2+\beta x+2c)y^{\prime }+(\beta -2b)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$898$	12617	$$(a{x}^3+b{x}^2+cx)y^{\prime \prime }+(\alpha x^2+\beta x+2c)y^{\prime }-(\alpha x+2b-\beta )y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$899$	12618	$$(a{x}^3+b{x}^2+cx)y^{\prime \prime }+(-2a{x}^2-(b+1)x+k)y^{\prime }+2(ax+1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$900$	12622	$$(a{x}^3+x^2+b)y^{\prime \prime }+a^{2}x(x^2-b)y^{\prime }-a^{3}bxy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$901$	12625	$$x(x-1)(x-a)y^{\prime \prime }+((\alpha +\beta +1)x^2-(\alpha +\beta +1+a(\gamma +d)-a)x+a\gamma )y^{\prime }+(\alpha \beta x-q)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$902$	12626	$$(a{x}^3+b{x}^2+cx+d)y^{\prime \prime }-(-{\lambda }^2+x^2)y^{\prime }+(x+\lambda )y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$903$	12628	$$2(a{x}^3+b{x}^2+cx+d)y^{\prime \prime }+3(3a{x}^2+2bx+c)y^{\prime }+(6ax+2b+\lambda )y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$904$	12630	$$(a{x}^3+b{x}^2+cx+d)y^{\prime \prime }+({\lambda }^3+x^3)y^{\prime }-({\lambda }^2-\lambda x+x^2)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$905$	12633	$$x^4{y}^{\prime \prime }+(a{x}^2+bx+c)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$906$	12639	$$a{x}^2{(x-1)}^2{y}^{\prime \prime }+(b{x}^2+cx+d)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$907$	12640	$$x^2(x^2+a)y^{\prime \prime }+(b{x}^2+c)x{y}^{\prime }+dy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$908$	12647	$${(x^2-1)}^2{y}^{\prime \prime }+2x(x^2-1)y^{\prime }-(\nu (\nu +1)(x^2-1)+n^2)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$909$	12648	$${(-x^2+1)}^2{y}^{\prime \prime }-2x(-x^2+1)y^{\prime }+(\nu (\nu +1)(-x^2+1)-{\mu }^2)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$910$	12649	$$a{(x^2-1)}^2{y}^{\prime \prime }+bx(x^2-1)y^{\prime }+(c{x}^2+dx+e)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$911$	12657	$${(x^2-1)}^2{y}^{\prime \prime }+2x(x^2-1)y^{\prime }+((x^2-1)(a^2{x}^2-\lambda )-m^2)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$912$	12658	$${(x^2+1)}^2{y}^{\prime \prime }+2x(x^2+1)y^{\prime }+((x^2+1)(a^2{x}^2-\lambda )+m^2)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$913$	12664	$$x^n{y}^{\prime \prime }+(ax+b)y^{\prime }-ay=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$914$	12665	$$x^n{y}^{\prime \prime }+(a{x}^{n-1}+bx)y^{\prime }+(a-1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$915$	12666	$$x^n{y}^{\prime \prime }+(2x^{n-1}+a{x}^2+bx)y^{\prime }+by=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$916$	12672	$$x(x^n+1)y^{\prime \prime }+((a-b)x^n+a-n)y^{\prime }+b(1-a)x^{n-1}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$917$	12674	$$x^2(a^2{x}^{2n}-1)y^{\prime \prime }+x(a^2(n+1)x^{2n}+n-1)y^{\prime }-\nu (\nu +1)a^2{n}^2{x}^{2n}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$918$	12675	$$x^2(a^2{x}^{2n}-1)y^{\prime \prime }+x(ap{x}^n+q)y^{\prime }+(ar{x}^n+s)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$919$	12676	$${(x^n+a)}^2{y}^{\prime \prime }-b{x}^{n-2}((b-1)x^n+a(n-1))y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$920$	12677	$${(a{x}^n+b)}^2{y}^{\prime \prime }+(a{x}^n+b)(c{x}^n+d)y^{\prime }+n(-ad+bc)x^{n-1}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$921$	12680	$$x^2{(a{x}^n+b)}^2{y}^{\prime \prime }+(n+1)x(a^2{x}^{2n}-b^2)y^{\prime }+cy=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$922$	12682	$$(a{x}^n+b{x}^m+c)y^{\prime \prime }+(\lambda -x)y^{\prime }+y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$923$	12683	$$(a{x}^n+b{x}^m+c)y^{\prime \prime }+({\lambda }^2-x^2)y^{\prime }+(x+\lambda )y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$924$	12688	$$y^{\prime \prime }+a(\lambda {\mathrm{e}}^{\lambda x}-a{\mathrm{e}}^{2\lambda x})y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$925$	12689	$$y^{\prime \prime }-(a^2{\mathrm{e}}^{2x}+a(2b+1){\mathrm{e}}^x+b^2)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$926$	12690	$$y^{\prime \prime }-(a{\mathrm{e}}^{2\lambda x}+b{\mathrm{e}}^{\lambda x}+c)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$927$	12691	$$y^{\prime \prime }+(a{\mathrm{e}}^{4\lambda x}+b{\mathrm{e}}^{3\lambda x}+c{\mathrm{e}}^{2\lambda x}-\frac{{\lambda }^2}{4})y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$928$	12692	$$y^{\prime \prime }+(a{\mathrm{e}}^{2\lambda x}{(b{\mathrm{e}}^{\lambda x}+c)}^n-\frac{{\lambda }^2}{4})y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$929$	12696	$$y^{\prime \prime }-y^{\prime }+(a{\mathrm{e}}^{3\lambda x}+b{\mathrm{e}}^{2\lambda x}+\frac{1}{4}-\frac{{\lambda }^2}{4})y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$930$	12697	$$y^{\prime \prime }-y^{\prime }+(a{\mathrm{e}}^{2\lambda x}{(b{\mathrm{e}}^{\lambda x}+c)}^n+\frac{1}{4}-\frac{{\lambda }^2}{4})y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$931$	12699	$$y^{\prime \prime }+(a+b){\mathrm{e}}^{\lambda x}{y}^{\prime }+a{\mathrm{e}}^{\lambda x}(b{\mathrm{e}}^{\lambda x}+\lambda )y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$932$	12700	$$y^{\prime \prime }+a{\mathrm{e}}^{\lambda x}{y}^{\prime }-b{\mathrm{e}}^{\mu x}(a{\mathrm{e}}^{\lambda x}+b{\mathrm{e}}^{\mu x}+\mu )y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$933$	12703	$$y^{\prime \prime }+(a{\mathrm{e}}^{2\lambda x}+\lambda )y^{\prime }-a\lambda {\mathrm{e}}^{2\lambda x}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$934$	12705	$$y^{\prime \prime }+(a{\mathrm{e}}^{\lambda x}+b)y^{\prime }+c(a{\mathrm{e}}^{\lambda x}+b-c)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$935$	12707	$$y^{\prime \prime }+(a+b{\mathrm{e}}^{\lambda x}+b-3\lambda )y^{\prime }+a^2\lambda (b-\lambda ){\mathrm{e}}^{2\lambda x}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$936$	12709	$$y^{\prime \prime }+(2a{\mathrm{e}}^{\lambda x}+b)y^{\prime }+(a^2{\mathrm{e}}^{2\lambda x}+a(b+\lambda ){\mathrm{e}}^{\lambda x}+c)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$937$	12710	$$y^{\prime \prime }+(a{\mathrm{e}}^{\lambda x}+2b-\lambda )y^{\prime }+(c{\mathrm{e}}^{2\lambda x}+ab{\mathrm{e}}^{\lambda x}+b^2-b\lambda )y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$938$	12711	$$y^{\prime \prime }+(a{\mathrm{e}}^x+b)y^{\prime }+(c(a-c){\mathrm{e}}^{2x}+(ak+bc-2ck+c){\mathrm{e}}^x+k(b-k))y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$939$	12712	$$y^{\prime \prime }+(a{\mathrm{e}}^{\lambda x}+b)y^{\prime }+(\alpha {\mathrm{e}}^{2\lambda x}+\beta {\mathrm{e}}^{\lambda x}+\gamma )y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$940$	12716	$$y^{\prime \prime }+{\mathrm{e}}^{\lambda x}(a{\mathrm{e}}^{2\mu x}+b)y^{\prime }+\mu ({\mathrm{e}}^{\lambda x}(b-a{\mathrm{e}}^{2\mu x})-\mu )y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$941$	12721	$$y^{\prime \prime }+a{\mathrm{e}}^{b{x}^n}{y}^{\prime }+c(a{\mathrm{e}}^{b{x}^n}-c)y=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✗
$942$	12725	$$(a{\mathrm{e}}^{\lambda x}+b)y^{\prime \prime }+(c{\mathrm{e}}^{\lambda x}+d)y^{\prime }+k((-ak+c){\mathrm{e}}^{\lambda x}+d-bk)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$943$	12726	$$(a{\mathrm{e}}^{\lambda x}+b)y^{\prime \prime }+(c{\mathrm{e}}^{\lambda x}+d)y^{\prime }+(n{\mathrm{e}}^{\lambda x}+m)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$944$	12796	$$(x^2+y^2)(y{y}^{\prime }+x)=(x^2+y^2+x)(y^{\prime }x-y)$$	[_rational]	✓	✓
$945$	12822	$$4{\mathrm{e}}^{2y}{y^{\prime }}^2+2y^{\prime }x-1=0$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$946$	12824	$${\mathrm{e}}^{2y}{y^{\prime }}^3+({\mathrm{e}}^{2x}+{\mathrm{e}}^{3x})y^{\prime }-{\mathrm{e}}^{3x}=0$$	[‘y=_G(x,y’)‘]	✓	✗
$947$	12840	$$x^2{y^{\prime }}^2-2x{y}^{\prime }y+y^2=x^2{y}^2+x^4$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$948$	12900	$$4x^2{y}^{\prime \prime }+4x^3{y}^{\prime }+(x^2+1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$949$	12915	$$x^2{y}^{\prime \prime }-2nx(x+1)y^{\prime }+(a^2{x}^2+n^2+n)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$950$	12916	$$x^4{y}^{\prime \prime }+2x^3(x+1)y^{\prime }+n^{2}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$951$	12926	$$(x^2-2x+2)y^{\prime \prime \prime }-x^2{y}^{\prime \prime }+2y^{\prime }x-2y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$952$	12927	$$x{y}^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }x+y=-x^2+1$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$953$	12932	$$2x^{3}y{y}^{\prime \prime \prime }+6x^3{y}^{\prime }{y}^{\prime \prime }+18x^{2}y{y}^{\prime \prime }+18x^2{y^{\prime }}^2+36x{y}^{\prime }y+6y^2=0$$	[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]	✓	✓
$954$	12935	$$x^2{y}^{\prime \prime \prime }-5x{y}^{\prime \prime }+(4x^4+5)y^{\prime }-8x^{3}y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$955$	12937	$$x^{2}y{y}^{\prime \prime }+{(y^{\prime }x-y)}^2=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$956$	12938	$$x^3{y}^{\prime \prime }-{(y^{\prime }x-y)}^2=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$957$	12939	$$y{y}^{\prime \prime }-{y^{\prime }}^2=y^2\ln \left(y\right)-x^2{y}^2$$	[[_2nd_order, _reducible, _mu_xy]]	✓	✓
$958$	12940	$$\sin {\left(x\right)}^2{y}^{\prime \prime }-2y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$959$	13008	$$x{x}^{\prime }=1-tx$$	[_rational, [_Abel, ‘2nd type‘, ‘class A‘]]	✓	✓
$960$	13320	$$y^{\prime \prime }+y^{\prime }x+x^{2}y=0$$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$961$	13594	$$t^3{x}^{\prime \prime \prime }-(t+3)t^2{x}^{\prime \prime }+2t(t+3)x^{\prime }-2(t+3)x=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$962$	13600	$$\sin \left(t\right)x^{\prime \prime }+\cos \left(t\right)x^{\prime }+2x=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$963$	13603	$$(t^4+t^2)x^{\prime \prime }+2t^3{x}^{\prime }+3x=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$964$	13604	$$x^{\prime \prime }-\tan \left(t\right)x^{\prime }+x=0$$	[_Lienard]	✓	✓
$965$	13871	$$y^{\prime \prime }=2y^3$$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓
$966$	13888	$$y^{\prime \prime \prime }+xy=\sin \left(x\right)$$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	✓
$967$	13889	$$y^{\prime \prime }+y{y}^{\prime }=1$$	[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$968$	13892	$$y^{\prime \prime \prime }+xy=\cosh \left(x\right)$$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	✓
$969$	13894	$$y^{\prime \prime \prime }+xy=\cosh \left(x\right)$$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	✓
$970$	13899	$$2y^{\prime \prime }+3y^{\prime }+4x^{2}y=1$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$971$	13914	$$y^{\prime \prime }+y^{\prime }\tan \left(x\right)+\cot \left(x\right)y=0$$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$972$	13915	$$(x^2+1)y^{\prime \prime }+(x-1)y^{\prime }+y=0$$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$973$	13918	$$y^{\prime \prime }-(x-1)y^{\prime }+x^{2}y=\tan \left(x\right)$$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$974$	13920	$$x^2{y}^{\prime \prime }-4x^2{y}^{\prime }+(x^2+1)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$975$	13921	$$y^{\prime \prime }+\frac{kx}{y^4}=0$$	[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]	✓	✗
$976$	13927	$$x^2{y}^{\prime \prime }+x^2{y}^{\prime }+2(1-x)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$977$	13945	$$(2\sin \left(x\right)-\cos \left(x\right))y^{\prime \prime }+(7\sin \left(x\right)+4\cos \left(x\right))y^{\prime }+10\cos \left(x\right)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$978$	14018	$$y^{\prime \prime }+3y^{\prime }+\frac{y}{t}=t$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$979$	14020	$$t^3{y}^{\prime \prime }-2y^{\prime }t+y=t^4$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$980$	14081	$$(-x^2+1)y^{\prime \prime }-2y^{\prime }x+n(n+1)y=0$$	[_Gegenbauer]	✓	✓
$981$	14413	$$\sqrt{1-x}{y}^{\prime \prime }-4y=\sin \left(x\right)$$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✗
$982$	15191	$$y^{\prime \prime }+x^2{y}^{\prime }-4y=x^3$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$983$	15192	$$y^{\prime \prime }+x^2{y}^{\prime }-4y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$984$	15193	$$y^{\prime \prime }+x^2{y}^{\prime }=4y$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$985$	15711	$$y{y}^{\prime }+y^4=\sin \left(x\right)$$	[‘y=_G(x,y’)‘]	✓	✗
$986$	15801	$$y^{\prime }=\sqrt{y^2-1}$$ i.c.	[_quadrature]	✓	✓
$987$	16040	$$y^{\prime }-2y=t^2\sqrt{y}$$ i.c.	[_Bernoulli]	✓	✓
$988$	16177	$${y^{\prime \prime }}^2-5y^{\prime \prime }{y}^{\prime }+4y^2=0$$	[[_2nd_order, _missing_x]]	✓	✗
$989$	16178	$${y^{\prime \prime }}^2-2y^{\prime \prime }{y}^{\prime }+y^2=0$$	[[_2nd_order, _missing_x]]	✓	✗
$990$	16569	$$x^{\prime \prime }+x=\{\begin{array}{cc}\cos \left(t\right)& 0\le t<\pi \\ 0& \pi \le t\end{array}$$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$991$	16603	$$y^{\prime }=\sin \left(xy\right)$$ i.c.	[‘y=_G(x,y’)‘]	✓	✓
$992$	16658	$$x^2{y}^{\prime }\cos \left(y\right)+1=0$$ i.c.	[_separable]	✓	✗
$993$	16659	$$x^2{y}^{\prime }+\cos \left(2y\right)=1$$ i.c.	[_separable]	✓	✗
$994$	16665	$$x^2{y}^{\prime }+\sin \left(2y\right)=1$$ i.c.	[_separable]	✓	✗
$995$	16702	$$y^{\prime }\sin \left(x\right)-\cos \left(x\right)y=-\frac{\sin {\left(x\right)}^2}{x^2}$$ i.c.	[_linear]	✓	✓
$996$	16704	$$2y^{\prime }x-y=1-\frac{2}{\sqrt{x}}$$ i.c.	[_linear]	✓	✓
$997$	16713	$$y^{\prime }-2y{\mathrm{e}}^x=2\sqrt{y{\mathrm{e}}^x}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$998$	16719	$$y^{\prime }=y({\mathrm{e}}^x+\ln \left(y\right))$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$999$	16721	$$y{y}^{\prime }+1=(x-1){\mathrm{e}}^{-\frac{y^2}{2}}$$	[‘y=_G(x,y’)‘]	✓	✓
$1000$	16722	$$y^{\prime }+\sin \left(2y\right)x=2x{\mathrm{e}}^{-x^2}\cos {\left(y\right)}^2$$	[‘y=_G(x,y’)‘]	✓	✓
$1001$	16781	$$(1+{y^{\prime }}^2)y^2-4y{y}^{\prime }-4x=0$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$1002$	16855	$$2y^{\prime \prime }=\frac{y^{\prime }}{x}+\frac{x^2}{y^{\prime }}$$ i.c.	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_poly_yn]]	✓	✓
$1003$	16870	$$3y^{\prime }{y}^{\prime \prime }=2y$$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✗
$1004$	16871	$$2y^{\prime \prime }=3y^2$$ i.c.	[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]	✓	✓
$1005$	16880	$$y^{\prime \prime \prime }=3y{y}^{\prime }$$ i.c.	[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]	✓	✗
$1006$	17041	$$y^{\prime \prime }+4y^{\prime }+3y=8{\mathrm{e}}^x+9$$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✗
$1007$	17043	$$y^{\prime \prime }+4y^{\prime }+4y=2{\mathrm{e}}^x(\sin \left(x\right)+7\cos \left(x\right))$$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✗
$1008$	17094	$$(1-x)y^{\prime \prime }+y^{\prime }x-y={(x-1)}^2{\mathrm{e}}^x$$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$1009$	17096	$$y^{\prime \prime }+\frac{2y^{\prime }}{x}-y=4{\mathrm{e}}^x$$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$1010$	17098	$$(x^2-2x)y^{\prime \prime }+(-x^2+2)y^{\prime }-2(1-x)y=2x-2$$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$1011$	17134	$$y^{\prime \prime \prime }+x\sin \left(y\right)=0$$ i.c. hint: series	[NONE]	✓	✓
$1012$	17476	$$(-x^2+1)y^{\prime \prime }-2y^{\prime }x+\alpha (\alpha +1)y=0$$	[_Gegenbauer]	✓	✓
$1013$	17487	$$(t-1)y^{\prime \prime }-3y^{\prime }t+4y=\sin \left(t\right)$$ i.c.	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$1014$	17488	$$t(t-4)y^{\prime \prime }+3y^{\prime }t+4y=2$$ i.c.	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$1015$	17849	$$y^{\prime }(x^2+y^2+3)=2x(2y-\frac{x^2}{y})$$	[_rational]	✓	✓
$1016$	17864	$$(x^2-x^3+3x{y}^2+2y^3)y^{\prime }+2x^3+3x^{2}y+y^2-y^3=0$$	[_rational]	✓	✓
$1017$	17866	$$x^2{y^{\prime }}^2-2x{y}^{\prime }y+y^2=x^2{y}^2+x^4$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$1018$	17908	$$n{x}^3{y}^{\prime \prime }={(y-y^{\prime }x)}^2$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$1019$	17909	$$y^2(x^2{y}^{\prime \prime }-y^{\prime }x+y)=x^3$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$1020$	17910	$$x^2{y}^2{y}^{\prime \prime }-3x{y}^2{y}^{\prime }+4y^3+x^6=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$1021$	17916	$$x^{2}y{y}^{\prime \prime }+x^2{y^{\prime }}^2-5x{y}^{\prime }y=4y^2$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$1022$	17919	$$40{y^{\prime \prime \prime }}^3-45y^{\prime \prime }{y}^{\prime \prime \prime }{y}^{\prime \prime \prime \prime }+9{y^{\prime \prime }}^2{y}^{\left(5\right)}=0$$	[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]]	✓	✓
$1023$	17924	$$(-x^2+1)y^{\prime \prime }-2y^{\prime }x+n(n+1)y=0$$	[_Gegenbauer]	✓	✓
$1024$	17926	$$\sin {\left(x\right)}^2{y}^{\prime \prime }=2y$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$1025$	17928	$$x{y}^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }x-y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$1026$	17932	$$(x^2+2)y^{\prime \prime \prime }-2x{y}^{\prime \prime }+(x^2+2)y^{\prime }-2xy=x^4+12$$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	✓
$1027$	17935	$$y^{\prime \prime }+\frac{y}{x^2\ln \left(x\right)}={\mathrm{e}}^x(\frac{2}{x}+\ln \left(x\right))$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$1028$	18123	$$(x^2+2y^{\prime })y^{\prime \prime }+2y^{\prime }x=0$$ i.c.	[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]]	✓	✓
$1029$	18210	$$y^{\prime \prime }-xf\left(x\right)y^{\prime }+f\left(x\right)y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$1030$	18212	$$x{y}^{\prime \prime }-(x+n)y^{\prime }+ny=0$$	[_Laguerre]	✓	✓
$1031$	18216	$$y^{\prime \prime }-f\left(x\right)y^{\prime }+(f\left(x\right)-1)y=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]	✓	✗
$1032$	18251	$$y^{\prime \prime }+3y^{\prime }x+x^{2}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$1033$	18460	$$x^2{y}^{\prime \prime }-\frac{x^2{y^{\prime }}^2}{2y}+4y^{\prime }x+4y=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$1034$	18463	$$\sin \left(x\right)y^{\prime \prime }+\cos \left(x\right)y^{\prime }+ny\sin \left(x\right)=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$1035$	18541	$$y^{\prime \prime \prime }{y}^{\prime }-3{y^{\prime \prime }}^2+3y^{\prime \prime }{y^{\prime }}^2-2{y^{\prime }}^4-x{y^{\prime }}^5=0$$	[[_3rd_order, _missing_y], [_3rd_order, _with_exponential_symmetries], [_3rd_order, _with_linear_symmetries]]	✓	✗
$1036$	18543	$$y^2{y}^{\prime \prime \prime }-(3y{y}^{\prime }+2x{y}^2)y^{\prime \prime }+(2{y^{\prime }}^2+2x{y}^{\prime }y+3x^2{y}^2)y^{\prime }+x^3{y}^3=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✗
$1037$	18551	$$(x^2+1)y^{\prime }+x^{2}y=x^3-x^2\arctan \left(x\right)$$	[_linear]	✓	✓
$1038$	18697	$$y^{\prime }x-y=x\sqrt{x^2+y^2}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$1039$	18758	$${(y^{\prime }x-y)}^2=a(1+{y^{\prime }}^2){(x^2+y^2)}^{3/2}$$	[[_1st_order, _with_linear_symmetries]]	✓	✓
$1040$	18759	$${(y^{\prime }x-y)}^2={y^{\prime }}^2-\frac{2y{y}^{\prime }}{x}+1$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$1041$	18773	$$(1-y^2+\frac{y^4}{x^2}){y^{\prime }}^2-\frac{2y{y}^{\prime }}{x}+\frac{y^2}{x^2}=0$$	[‘y=_G(x,y’)‘]	✓	✗
$1042$	18860	$${(5+2x)}^2{y}^{\prime \prime }-6(5-2x)y^{\prime }+8y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$1043$	18868	$$16{(x+1)}^4{y}^{\prime \prime \prime \prime }+96{(x+1)}^3{y}^{\prime \prime \prime }+104{(x+1)}^2{y}^{\prime \prime }+8(x+1)y^{\prime }+y=x^2+4x+3$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$1044$	18880	$$\sqrt{x}{y}^{\prime \prime }+2y^{\prime }x+3y=x$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$1045$	18927	$$\sin {\left(x\right)}^2{y}^{\prime \prime }=2y$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$1046$	18951	$$y^{\prime \prime }-2b{y}^{\prime }+b^2{x}^{2}y=0$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$1047$	18956	$$x^2{y}^{\prime \prime \prime }+x^2{y}^{\prime \prime }-2y^{\prime }x+2y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$1048$	18962	$$x^{2}y{y}^{\prime \prime }+{(y^{\prime }x-y)}^2=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$1049$	19034	$$y^{\prime }-\frac{\tan \left(y\right)}{x+1}=(x+1){\mathrm{e}}^x\sec \left(y\right)$$	[‘y=_G(x,y’)‘]	✓	✓
$1050$	19040	$$y^{\prime }+\frac{\tan \left(y\right)}{x}=\frac{\tan \left(y\right)\sin \left(y\right)}{x^2}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$1051$	19061	$$y^{\prime }x-y=x\sqrt{x^2+y^2}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$1052$	19078	$$y^{\prime }={\mathrm{e}}^{x-y}({\mathrm{e}}^x-{\mathrm{e}}^y)$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]	✓	✓
$1053$	19080	$$y^{\prime }+\frac{\tan \left(y\right)}{x}=\frac{\tan \left(y\right)\sin \left(y\right)}{x^2}$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$1054$	19190	$${(y^{\prime }x-y)}^2=a(1+{y^{\prime }}^2){(x^2+y^2)}^{3/2}$$	[[_1st_order, _with_linear_symmetries]]	✓	✓
$1055$	19193	$${(y^{\prime }x-y)}^2={y^{\prime }}^2-\frac{2y{y}^{\prime }}{x}+1$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$1056$	19227	$$(-a^2+x^2){y^{\prime }}^2-2x{y}^{\prime }y-x^2=0$$	[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]]	✓	✓
$1057$	19232	$${(1-y^{\prime })}^2-{\mathrm{e}}^{-2y}={\mathrm{e}}^{-2x}{y^{\prime }}^2$$	[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$1058$	19289	$$x^2{y}^{\prime \prime \prime }+4x{y}^{\prime \prime }+(x^2+2)y^{\prime }+3xy=2$$	[[_3rd_order, _linear, _nonhomogeneous]]	✓	✓
$1059$	19337	$$y^{\prime }=x{y}^{\prime \prime }+\sqrt{1+{y^{\prime }}^2}$$	[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]	✓	✓
$1060$	19345	$$2x^{2}y{y}^{\prime \prime }+y^2=x^2{y^{\prime }}^2$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$1061$	19347	$$x^4{y}^{\prime \prime }=(x^3+2xy)y^{\prime }-4y^2$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$1062$	19348	$$x^4{y}^{\prime \prime }-x^3{y}^{\prime }=x^2{y^{\prime }}^2-4y^2$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$1063$	19370	$$y^{\prime \prime \prime }-x{y}^{\prime \prime }-y^{\prime }+xy=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$1064$	19410	$$x^{2}y{y}^{\prime \prime }+{(y^{\prime }x-y)}^2=0$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$1065$	19433	$$x{y}^{\prime \prime }+(x^2+1)y^{\prime }+2xy=2x$$ i.c.	[[_2nd_order, _exact, _linear, _nonhomogeneous]]	✓	✓
$1066$	19451	$$y^{\prime }+\sin \left(2y\right)x=x^3\cos {\left(y\right)}^2$$	[‘y=_G(x,y’)‘]	✓	✓
$1067$	19474	$$x^2({y^{\prime }}^2-y^2)+y^2=x^4+2x{y}^{\prime }y$$	[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]	✓	✓
$1068$	19493	$$(1-y^2+\frac{y^4}{x^2}){y^{\prime }}^2-\frac{2y{y}^{\prime }}{x}+\frac{y^2}{x^2}=0$$	[‘y=_G(x,y’)‘]	✓	✗
$1069$	19515	$${(2x-1)}^3{y}^{\prime \prime \prime }+(2x-1)y^{\prime }-2y=0$$	[[_3rd_order, _with_linear_symmetries]]	✓	✓
$1070$	19517	$$16{(x+1)}^4{y}^{\prime \prime \prime \prime }+96{(x+1)}^3{y}^{\prime \prime \prime }+104{(x+1)}^2{y}^{\prime \prime }+8(x+1)y^{\prime }+y=x^2+4x+3$$	[[_high_order, _with_linear_symmetries]]	✓	✓
$1071$	19519	$$2x^{2}y{y}^{\prime \prime }+4y^2=x^2{y^{\prime }}^2+2x{y}^{\prime }y$$	[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$1072$	19525	$$\sqrt{x}{y}^{\prime \prime }+2y^{\prime }x+3y=x$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$1073$	19527	$$2x^2\cos \left(y\right)y^{\prime \prime }-2x^2\sin \left(y\right){y^{\prime }}^2+x\cos \left(y\right)y^{\prime }-\sin \left(y\right)=\ln \left(x\right)$$	[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]	✓	✓
$1074$	19541	$$x^4{y}^{\prime \prime }={(y-y^{\prime }x)}^3$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$1075$	19544	$$\sin {\left(x\right)}^2{y}^{\prime \prime }=2y$$	[[_2nd_order, _with_linear_symmetries]]	✓	✓
$1076$	19547	$$y^{\prime \prime }-\cot \left(x\right)y^{\prime }-(1-\cot \left(x\right))y={\mathrm{e}}^x\sin \left(x\right)$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓
$1077$	19549	$$y^{\prime \prime }+(1+\frac{2\cot \left(x\right)}{x}-\frac{2}{x^2})y=x\cos \left(x\right)$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✗
$1078$	19566	$$y^{\prime \prime }+(1-\cot \left(x\right))y^{\prime }-\cot \left(x\right)y=\sin {\left(x\right)}^2$$	[[_2nd_order, _linear, _nonhomogeneous]]	✓	✓