$$y^{\prime \prime }+4y^{\prime }+5y=(1-\mathrm{Heaviside}(t-10)){\mathrm{e}}^t-{\mathrm{e}}^{10}\delta (t-10)$$

$$y^{\prime \prime }+5y^{\prime }+6y=\delta (t-\frac{\pi }{2})+\mathrm{Heaviside}(t-\pi )\cos \left(t\right)$$

$$y^{\prime \prime }+5y^{\prime }+6y=\mathrm{Heaviside}(-1+t)+\delta (t-2)$$

$$y^{\prime \prime }+2y^{\prime }+5y=25t-100\delta (t-\pi )$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }-4y=0$$

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

$$y^{\prime \prime }+16y=0$$

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

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

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

$$y^{\prime \prime }+(-1+3i)y^{\prime }-3iy=0$$

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

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

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

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

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

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

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

$$y^{\prime \prime }+(1+4i)y^{\prime }+y=0$$

$$y^{\prime \prime }+(-1+3i)y^{\prime }-3iy=0$$

$$y^{\prime \prime }+10y=0$$

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

$$y^{\prime \prime }+9y=\sin \left(3x\right)$$

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

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

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

$$y^{\prime \prime }-7y^{\prime }+6y=\sin \left(x\right)$$

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

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

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

$$6y^{\prime \prime }+5y^{\prime }-6y=x$$

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }+9y=x^2{\mathrm{e}}^{3x}$$

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

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

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

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

$${(3x-1)}^2{y}^{\prime \prime }+(9x-3)y^{\prime }-9y=0$$

$$x^2{y}^{\prime \prime }-7x{y}^{\prime }+15y=0$$