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

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

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

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

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

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

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

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

$$y^{\prime \prime \prime }-8y=0$$

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

$$y^{\prime \prime \prime }-5y^{\prime \prime }+6y^{\prime }=0$$

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

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

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

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

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

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

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

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

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

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

$$y^{\left(5\right)}+2y=0$$

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

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

$$y^{\prime \prime \prime }-i{y}^{\prime \prime }+y^{\prime }-iy=0$$

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

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

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

$$y^{\prime \prime \prime }-8y={\mathrm{e}}^{ix}$$

$$y^{\prime \prime \prime \prime }+16y=\cos \left(x\right)$$

$$y^{\prime \prime \prime \prime }-4y^{\prime \prime \prime }+6y^{\prime \prime }-4y^{\prime }+y={\mathrm{e}}^x$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }+8y=0$$

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

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

$$y^{\prime \prime }-9y^{\prime }+20y=0$$

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

$$4y^{\prime \prime }-12y^{\prime }+9y=0$$

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

$$y^{\prime \prime }-6y^{\prime }+25y=0$$

$$4y^{\prime \prime }+20y^{\prime }+25y=0$$

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

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

$$4y^{\prime \prime }-8y^{\prime }+7y=0$$

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

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

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

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

$$y^{\prime \prime }-5y^{\prime }+6y=0$$

$$y^{\prime \prime }-6y^{\prime }+5y=0$$

$$y^{\prime \prime }-6y^{\prime }+9y=0$$

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

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

$$y^{\prime \prime }+8y^{\prime }-9y=0$$

$$y^{\prime \prime }+3y^{\prime }-10y=6{\mathrm{e}}^{4x}$$

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

$$y^{\prime \prime }+10y^{\prime }+25y=14{\mathrm{e}}^{-5x}$$

$$y^{\prime \prime }-2y^{\prime }+5y=25x^2+12$$

$$y^{\prime \prime }-y^{\prime }-6y=20{\mathrm{e}}^{-2x}$$

$$y^{\prime \prime }-3y^{\prime }+2y=14\sin \left(2x\right)-18\cos \left(2x\right)$$

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

$$y^{\prime \prime }-2y^{\prime }=12x-10$$

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

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

$$y^{\prime \prime }+y^{\prime }=10x^4+2$$

$$y^{\prime \prime }+4y=4\cos \left(2x\right)+6\cos \left(x\right)+8x^2-4x$$

$$y^{\prime \prime }+9y=2\sin \left(3x\right)+4\sin \left(x\right)-26{\mathrm{e}}^{-2x}+27x^3$$

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

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

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

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

$$y^{\prime \prime }-2y^{\prime }-3y=64x{\mathrm{e}}^{-x}$$

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

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

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

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

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

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

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

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