$$2y+(x^{2}y+1)x{y}^{\prime }=0$$

$$y(xy+1)+(1-xy)x{y}^{\prime }=0$$

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

$$(x^2-y^4)y^{\prime }-xy=0$$

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

$$x(2-9x{y}^2)+y(4y^2-6x^3)y^{\prime }=0$$

$$\frac{y}{x}+(y^3+\ln \left(x\right))y^{\prime }=0$$

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

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

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

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

$$(x^2+1)y^{\prime \prime }+x{y}^{\prime }+y=0$$

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

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

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

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

$$y^{\prime \prime \prime }-2x{y}^{\prime \prime }+4x^2{y}^{\prime }+8x^{3}y=0$$

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

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

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

$$(x^2+1)y^{\prime \prime }+x{y}^{\prime }+y=0$$

$$y^{\prime \prime }+x{y}^{\prime }+y=2x{\mathrm{e}}^x-1$$

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

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

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

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

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

$$x^2(1+x)y^{\prime \prime }+x(4x+3)y^{\prime }-y=x+\frac{1}{x}$$

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

$$x{y}^{\prime \prime }+2y^{\prime }+xy=\sec \left(x\right)$$

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

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

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

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

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

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

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

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

$${\mathrm{e}}^x+y+(x-2\sin \left(y\right))y^{\prime }=0$$

$$3x+\frac{6}{y}+(\frac{x^2}{y}+\frac{3y}{x})y^{\prime }=0$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$p{x}^2{u}^{\prime \prime }+qx{u}^{\prime }+ru=f\left(x\right)$$

$$\sin \left(x\right)u^{\prime \prime }+2\cos \left(x\right)u^{\prime }+\sin \left(x\right)u=0$$

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

$$y^{\prime \prime }-\frac{x{y}^{\prime }}{-x^2+1}+\frac{y}{-x^2+1}=0$$

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

$$y^{\prime \prime \prime }-3y^{\prime \prime }+3y^{\prime }-y=4{\mathrm{e}}^t$$

$$y^{\prime \prime \prime \prime }+2y^{\prime \prime }+y=3\sin \left(t\right)-5\cos \left(t\right)$$

$$y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y=g\left(t\right)$$

$$y^{\left(5\right)}-\frac{y^{\prime \prime \prime \prime }}{t}=0$$

$$x{x}^{\prime \prime }-{x^{\prime }}^2=0$$

$$y^{\prime \prime \prime \prime }+4y^{\prime \prime \prime }+3y^{\prime \prime }-4y^{\prime }-4y=f\left(x\right)$$

$$u^{\prime \prime }-(2x+1)u^{\prime }+(x^2+x-1)u=0$$

$$y^{\prime \prime }+6y^{\prime }+9y=50{\mathrm{e}}^{2x}$$

$$y^{\prime \prime }-4y^{\prime }+4y=50{\mathrm{e}}^{2x}$$

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

$$y^{\prime \prime \prime }+6y^{\prime \prime }+11y^{\prime }+6y=2\sin \left(3x\right)$$

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

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

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

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

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

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

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

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

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

$$\frac{1}{y}+\sec \left(\frac{y}{x}\right)-\frac{x{y}^{\prime }}{y^2}=0$$

$${\varphi }^{\prime }-\frac{{\varphi }^2}{2}-\varphi \cot \left(\theta \right)=0$$

$$u^{\prime \prime }-\cot \left(\theta \right)u^{\prime }=0$$

$$({\varphi }^{\prime }-\frac{{\varphi }^2}{2})\sin {\left(\theta \right)}^2-\varphi \sin \left(\theta \right)\cos \left(\theta \right)=\frac{\cos \left(2\theta \right)}{2}+1$$

$$a{y}^{\prime \prime }{y}^{\prime \prime \prime }=\sqrt{1+{y^{\prime \prime }}^2}$$

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

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

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

$$y^{\prime \prime }-\frac{y^{\prime }}{\sqrt{x}}+\frac{(x+\sqrt{x}-8)y}{4x^2}=0$$

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

$$(-x^2+1){\eta }^{\prime \prime }-(1+x){\eta }^{\prime }+(k+1)\eta =0$$

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

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

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

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

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

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

$$[x_1^{\prime }\left(t\right)=3x_1\left(t\right)-18x_2\left(t\right),x_2^{\prime }\left(t\right)=2x_1\left(t\right)-9x_2\left(t\right)]$$

$$[x_1^{\prime }\left(t\right)=x_1\left(t\right)+3x_2\left(t\right),x_2^{\prime }\left(t\right)=5x_1\left(t\right)+3x_2\left(t\right)]$$

$$[x_1^{\prime }\left(t\right)=-x_1\left(t\right)+3x_2\left(t\right),x_2^{\prime }\left(t\right)=-3x_1\left(t\right)+5x_2\left(t\right)]$$