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

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

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

$$8{(1+y^{\prime })}^3=27(x+y){(-y^{\prime }+1)}^3$$

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

$$x^4{y}^{\prime \prime }+2x^3(1+x)y^{\prime }+n^{2}y=0$$

$$y^{\prime \prime }+2\cot \left(x\right)y^{\prime }+2\tan \left(x\right){y^{\prime }}^2=0$$

$$\frac{1+8x{y}^{\frac{2}{3}}}{x^{\frac{2}{3}}{y}^{\frac{1}{3}}}+\frac{(2x^{\frac{4}{3}}{y}^{\frac{2}{3}}-x^{\frac{1}{3}})y^{\prime }}{y^{\frac{4}{3}}}=0$$

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

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

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

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

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

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

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

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

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

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

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

$$\sqrt{1-x}{y}^{\prime \prime }-4y=\sin \left(x\right)$$

$$S^{\prime }=S^3-2S^2+S$$

$$S^{\prime }=S^3-2S^2+S$$

$$S^{\prime }=S^3-2S^2+S$$

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

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

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

$$w^{\prime }=w\cos \left(w\right)$$

$$w^{\prime }=w\cos \left(w\right)$$

$$w^{\prime }=w\cos \left(w\right)$$

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

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

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

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

$$1=\cos \left(y\right)y^{\prime }$$

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

$$y^4+(t^4-t{y}^3)y^{\prime }=0$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$y^{\prime }=y^{\frac{2}{3}}+a$$

$$8{y^{\prime }}^3-12{y^{\prime }}^2=27y-27x$$

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

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

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

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

$$y^{\prime \prime }+4y^{\prime }+3y=8{\mathrm{e}}^x+9$$

$$y^{\prime \prime }+4y^{\prime }+4y=2{\mathrm{e}}^x(\sin \left(x\right)+7\cos \left(x\right))$$

$$y^{\prime \prime }-5y^{\prime }+6y=2{\mathrm{e}}^{-2x}(9\sin \left(2x\right)+4\cos \left(2x\right))$$

$$y^{\prime \prime }-4y^{\prime }+4y={\mathrm{e}}^{-x}(9x^2+5x-12)$$

$$2x^2(2-\ln \left(x\right))y^{\prime \prime }+x(4-\ln \left(x\right))y^{\prime }-y=\frac{{(2-\ln \left(x\right))}^2}{\sqrt{x}}$$

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

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

$$[x^{\prime }\left(t\right)=\frac{t+y\left(t\right)}{y\left(t\right)+x\left(t\right)},y^{\prime }\left(t\right)=\frac{t+x\left(t\right)}{y\left(t\right)+x\left(t\right)}]$$

$$[x^{\prime \prime }\left(t\right)=x{\left(t\right)}^2+y\left(t\right),y^{\prime }\left(t\right)=-2x\left(t\right)x^{\prime }\left(t\right)+x\left(t\right)]$$