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

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }\sin \left(x\right)+x{y}^{\prime }+7y=1$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$x{y}^{\prime \prime }+(6x{y}^2+1)y^{\prime }+2y^3+1=0$$

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

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

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

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

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

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

$$(x^2+2x)y^{\prime \prime }+(x^2+x+10)y^{\prime }=(25-6x)y$$

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

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

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

$$(2\sin \left(x\right)-\cos \left(x\right))y^{\prime \prime }+(7\sin \left(x\right)+4\cos \left(x\right))y^{\prime }+10\cos \left(x\right)y=0$$

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

$$y^{\prime \prime }+(2x+5)y^{\prime }+(4x+8)y={\mathrm{e}}^{-2x}$$

$$t^2{y}^{\prime \prime }+3t{y}^{\prime }+y=t^7$$

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

$$y^{\prime \prime }+3y^{\prime }+\frac{y}{t}=t$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$x^{\prime \prime }+x+x^3=0$$

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

$$x^{\prime \prime }+x^{\prime }+x+x^3=0$$

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

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

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

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

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

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

$$x^2{y}^{\prime \prime }+6x{y}^{\prime }+4y=0$$

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

$$x^3{y}^{\prime \prime \prime }-3x^2{y}^{\prime \prime }+6x{y}^{\prime }-6y=0$$

$$x^2{y}^{\prime \prime }-4x{y}^{\prime }+6y=0$$

$$x^2{y}^{\prime \prime }-4x{y}^{\prime }+6y=0$$

$$x^2{y}^{\prime \prime }-4x{y}^{\prime }+6y=0$$

$$x^2{y}^{\prime \prime }-4x{y}^{\prime }+6y=0$$

$$x^2{y}^{\prime \prime }-4x{y}^{\prime }+6y=0$$

$$x^2{y}^{\prime \prime }-4x{y}^{\prime }+6y=0$$

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

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

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

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

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

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

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

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

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

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

$$y^2{y}^{\prime \prime }=8x^2$$