$$y^{\prime }+\frac{xy}{a^2+x^2}=x$$

$$y^{\prime }=\frac{4y^2}{x^2}-y^2$$

$$y^{\prime }-\frac{y}{x}=1$$

$$y^{\prime }-y\tan \left(x\right)=1$$

$$y^{\prime }-\frac{y^2}{x^2}=\frac{1}{4}$$

$$y^{\prime }-\frac{y^2}{x^2}=\frac{1}{4}$$

$$y^{\prime }\sin \left(x\right)+2\cos \left(x\right)y=1$$

$$(5x+y-7)y^{\prime }=3+3x+3y$$

$$x{y}^{\prime }+y-\frac{y^2}{x^{\frac{3}{2}}}=0$$

$$(2\sin \left(y\right)-x)y^{\prime }=\tan \left(y\right)$$

$$(2\sin \left(y\right)-x)y^{\prime }=\tan \left(y\right)$$

$$y^{\prime \prime }+{y^{\prime }}^2+y^{\prime }=0$$

$$x^{\prime \prime }+{\omega }_0^{2}x=a\cos \left(\omega t\right)$$

$$f^{\prime \prime }+2f^{\prime }+5f=0$$

$$f^{\prime \prime }+2f^{\prime }+5f={\mathrm{e}}^{-t}\cos \left(3t\right)$$

$$f^{\prime \prime }+6f^{\prime }+9f={\mathrm{e}}^{-t}$$

$$f^{\prime \prime }+8f^{\prime }+12f=12{\mathrm{e}}^{-4t}$$

$$f^{\prime \prime }+8f^{\prime }+12f=12{\mathrm{e}}^{-4t}$$

$$y^{\prime \prime }+2y^{\prime }+y=4{\mathrm{e}}^{-x}$$

$$y^{\prime \prime \prime }-12y^{\prime }+16y=32x-8$$

$$\frac{y^{\prime \prime }}{y}-\frac{{y^{\prime }}^2}{y^2}+\frac{2a\coth \left(2ax\right)y^{\prime }}{y}=2a^2$$

$$x^2{y}^{\prime \prime }-x{y}^{\prime }+y=x$$

$${(1+x)}^2{y}^{\prime \prime }+3(1+x)y^{\prime }+y=x^2$$

$$(-2+x)y^{\prime \prime }+3y^{\prime }+\frac{4y}{x^2}=0$$

$$y^{\prime \prime }-y=x^n$$

$$y^{\prime \prime }-2y^{\prime }+y=2x{\mathrm{e}}^x$$

$$2y{y}^{\prime \prime \prime }+2(y+3y^{\prime })y^{\prime \prime }+2{y^{\prime }}^2=\sin \left(x\right)$$

$$x{y}^{\prime \prime \prime }+2y^{\prime \prime }=Ax$$

$$y^{\prime \prime }+4x{y}^{\prime }+(4x^2+6)y={\mathrm{e}}^{-x^2}\sin \left(2x\right)$$

$$(-z^2+1)y^{\prime \prime }-3z{y}^{\prime }+\lambda y=0$$

$$4z{y}^{\prime \prime }+2(1-z)y^{\prime }-y=0$$

$$z{y}^{\prime \prime }-2y^{\prime }+9z^{5}y=0$$

$$f^{\prime \prime }+2(z-1)f^{\prime }+4f=0$$

$$z^2{y}^{\prime \prime }-\frac{3z{y}^{\prime }}{2}+(1+z)y=0$$

$$z{y}^{\prime \prime }-2y^{\prime }+zy=0$$

$$y^{\prime \prime }-2z{y}^{\prime }-2y=0$$

$$z(1-z)y^{\prime \prime }+(1-z)y^{\prime }+\lambda y=0$$

$$z{y}^{\prime \prime }+(2z-3)y^{\prime }+\frac{4y}{z}=0$$

$$(z^2+5z+6)y^{\prime \prime }+2y=0$$

$$(z^2+5z+7)y^{\prime \prime }+2y=0$$

$$y^{\prime \prime }+\frac{y}{z^3}=0$$

$$z{y}^{\prime \prime }+(1-z)y^{\prime }+\lambda y=0$$

$$(-z^2+1)y^{\prime \prime }-z{y}^{\prime }+m^{2}y=0$$

$$y^{\prime }=2xy$$

$$y^{\prime }=\frac{y^2}{x^2+1}$$

$${\mathrm{e}}^{x+y}{y}^{\prime }-1=0$$

$$y^{\prime }=\frac{y}{x\ln \left(x\right)}$$

$$y-(-2+x)y^{\prime }=0$$

$$y^{\prime }=\frac{2x(y-1)}{x^2+3}$$

$$y-x{y}^{\prime }=3-2x^2{y}^{\prime }$$

$$y^{\prime }=\frac{\cos (x-y)}{\sin \left(x\right)\sin \left(y\right)}-1$$

$$y^{\prime }=\frac{x(y^2-1)}{2(-2+x)(-1+x)}$$

$$y^{\prime }=\frac{x^{2}y-32}{-x^2+16}+32$$

$$(x-a)(x-b)y^{\prime }-y+c=0$$

$$(x^2+1)y^{\prime }+y^2=-1$$

$$(-x^2+1)y^{\prime }+xy=ax$$

$$y^{\prime }=1-\frac{\sin (x+y)}{\sin \left(y\right)\cos \left(x\right)}$$

$$y^{\prime }=y^3\sin \left(x\right)$$

$$y^{\prime }-y={\mathrm{e}}^{2x}$$

$$x^2{y}^{\prime }-4xy=x^7\sin \left(x\right)$$

$$y^{\prime }+2xy=2x^3$$

$$y^{\prime }+\frac{2xy}{x^2+1}=4x$$

$$y^{\prime }+\frac{2xy}{x^2+1}=\frac{4}{{(x^2+1)}^2}$$

$$2\cos {\left(x\right)}^2{y}^{\prime }+y\sin \left(2x\right)=4\cos {\left(x\right)}^4$$

$$y^{\prime }+\frac{y}{x\ln \left(x\right)}=9x^2$$

$$y^{\prime }-y\tan \left(x\right)=8\sin {\left(x\right)}^3$$

$$t{x}^{\prime }+2x=4{\mathrm{e}}^t$$

$$y^{\prime }=\sin \left(x\right)(y\sec \left(x\right)-2)$$

$$1-y\sin \left(x\right)-\cos \left(x\right)y^{\prime }=0$$

$$y^{\prime }-\frac{y}{x}=2x^2\ln \left(x\right)$$

$$y^{\prime }+\alpha y={\mathrm{e}}^{\beta x}$$

$$y^{\prime }+\frac{m}{x}=\ln \left(x\right)$$

$$(3x-y)y^{\prime }=3y$$

$$y^{\prime }=\frac{{(x+y)}^2}{2x^2}$$

$$\sin \left(\frac{y}{x}\right)(-y+x{y}^{\prime })=x\cos \left(\frac{y}{x}\right)$$

$$x{y}^{\prime }=\sqrt{16x^2-y^2}+y$$

$$-y+x{y}^{\prime }=\sqrt{9x^2+y^2}$$

$$x(x^2-y^2)-x(x^2+y^2)y^{\prime }=0$$

$$x{y}^{\prime }+y\ln \left(x\right)=y\ln \left(y\right)$$

$$y^{\prime }=\frac{y^2+2xy-2x^2}{x^2-xy+y^2}$$

$$2xy{y}^{\prime }-x^2{\mathrm{e}}^{-\frac{y^2}{x^2}}-2y^2=0$$

$$x^2{y}^{\prime }=y^2+3xy+x^2$$

$$y{y}^{\prime }=\sqrt{x^2+y^2}-x$$

$$2x(y+2x)y^{\prime }=y(4x-y)$$

$$x{y}^{\prime }=x\tan \left(\frac{y}{x}\right)+y$$

$$y^{\prime }=\frac{x\sqrt{x^2+y^2}+y^2}{xy}$$

$$y^{\prime \prime }-25y=0$$

$$y^{\prime \prime }+4y=0$$

$$y^{\prime \prime }+y^{\prime }-2y=0$$

$$y^{\prime }=-y^2$$

$$y^{\prime }=\frac{y}{2x}$$

$$y^{\prime \prime }+2y^{\prime }+5y=0$$

$$y^{\prime \prime }-9y=0$$

$$x^2{y}^{\prime \prime }+5x{y}^{\prime }+3y=0$$

$$x^2{y}^{\prime \prime }-3x{y}^{\prime }+4y=0$$

$$x^2{y}^{\prime \prime }-3x{y}^{\prime }+13y=0$$

$$2x^2{y}^{\prime \prime }-x{y}^{\prime }+y=9x^2$$

$$x^2{y}^{\prime \prime }-4x{y}^{\prime }+6y=x^4\sin \left(x\right)$$

$$y^{\prime \prime }-(a+b)y^{\prime }+aby=0$$

$$y^{\prime \prime }-2a{y}^{\prime }+a^{2}y=0$$