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

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

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

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

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

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

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

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

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

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

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

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

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

$${y^{\prime \prime }}^2-5y^{\prime \prime }{y}^{\prime }+4y^2=0$$

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

$${\mathrm{e}}^{-2t}(y{y}^{\prime \prime }-{y^{\prime }}^2)-2t(t+1)y=0$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$y^3{y}^{\prime \prime }=-1$$

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

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

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

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

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

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

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

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

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

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

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