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

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

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

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

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

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

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

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

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

$$4x^2{y}^{\prime \prime }+y=8\sqrt{x}(\ln \left(x\right)+1)$$

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

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

$$y^{\prime \prime }+20y^{\prime }+500y=100000\cos \left(100x\right)$$

$$4x^2{y}^{\prime \prime }+(-8x^2+4x)y^{\prime }+(4x^2-4x-1)y=4\sqrt{x}{\mathrm{e}}^x$$

$$x{y}^{\prime \prime }-(2x+2)y^{\prime }+(2+x)y=6x^3{\mathrm{e}}^x$$

$$y^{\prime \prime }+2y^{\prime }-24y=16-(2+x){\mathrm{e}}^{4x}$$

$$y^{\prime \prime }+3y^{\prime }-4y=6{\mathrm{e}}^{2t-2}$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$x^6{y}^{\prime \prime }+3x^5{y}^{\prime }+a^{2}y=\frac{1}{x^2}$$

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

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

$$x{y}^{\prime \prime }-y^{\prime }+4x^{3}y=8x^3\sin {\left(x\right)}^2$$

$$x{y}^{\prime \prime }-y^{\prime }+4x^{3}y=x^5$$

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

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

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

$$y^{\prime \prime }-4x{y}^{\prime }+(4x^2-1)y=-3{\mathrm{e}}^{x^2}\sin \left(x\right)$$

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

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

$$y^{\prime \prime }-2\tan \left(x\right)y^{\prime }+5y={\mathrm{e}}^{x^2}\sec \left(x\right)$$

$$y^{\prime }+a{\varphi }^{\prime }\left(x\right)y^3+6a\varphi \left(x\right)y^2+\frac{(2a+1)y{\varphi }^{\prime \prime }\left(x\right)}{{\varphi }^{\prime }\left(x\right)}+2+2a=0$$

$$y^{\prime \prime }+y-\sin \left(nx\right)=0$$

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

$$y^{\prime \prime }+y-\sin \left(ax\right)\sin \left(bx\right)=0$$

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

$$y^{\prime \prime }+a^{2}y-\cot \left(ax\right)=0$$

$$y^{\prime \prime }+a{y}^{\prime }+by-f\left(x\right)=0$$

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

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

$$y^{\prime \prime }+y^{\prime }\sqrt{x}+(\frac{1}{4\sqrt{x}}+\frac{x}{4}-9)y-x{\mathrm{e}}^{-\frac{x^{\frac{3}{2}}}{3}}=0$$

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

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

$$y^{\prime \prime }+f\left(x\right)y^{\prime }+(f^{\prime }\left(x\right)+a)y-g\left(x\right)=0$$

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

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

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

$$x{y}^{\prime \prime }+(4x^2-1)y^{\prime }-4x^{3}y-4x^5=0$$

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

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

$$x^2{y}^{\prime \prime }+x{y}^{\prime }+(-v^2+x^2)y-f\left(x\right)=0$$

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

$$x^2{y}^{\prime \prime }-2x{y}^{\prime }+2y-x^5\ln \left(x\right)=0$$

$$x^2{y}^{\prime \prime }-2x{y}^{\prime }-4y-x\sin \left(x\right)-(x^{2}a+12a+4)\cos \left(x\right)=0$$

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

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

$$x^2{y}^{\prime \prime }+3x{y}^{\prime }+(-v^2+x^2+1)y-f\left(x\right)=0$$

$$x^2{y}^{\prime \prime }-3x{y}^{\prime }+4y-5x=0$$

$$x^2{y}^{\prime \prime }-3x{y}^{\prime }-5y-x^2\ln \left(x\right)=0$$

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

$$x^2{y}^{\prime \prime }-5x{y}^{\prime }+8y-\sin \left(x\right)x^3=0$$

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

$$(x^2-1)y^{\prime \prime }-n(n+1)y+\frac{\partial }{\partial x}\mathrm{LegendreP}(n,x)=0$$

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

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

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

$$x(x+3)y^{\prime \prime }+(3x-1)y^{\prime }+y-(20x+30){(x^2+3x)}^{\frac{7}{3}}=0$$

$$4x^2{y}^{\prime \prime }+4x{y}^{\prime }-(4x^2+1)y-4\sqrt{x^3}{\mathrm{e}}^x=0$$

$$4x^2{y}^{\prime \prime }+5x{y}^{\prime }-y-\ln \left(x\right)=0$$