$$y^{\prime \prime }+4y=\{\begin{array}{cc}8t& 0\le t<\frac{\pi }{2}\\ 8\pi & \frac{\pi }{2}\le t\end{array}$$

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

$$y^{\prime \prime }+2y^{\prime }+2y=3\delta (-1+t)$$

$$y^{\prime \prime }+4y^{\prime }+29y=5\delta (t-\pi )-5\delta (t-2\pi )$$

$$y^{\prime \prime }+3y^{\prime }+2y=1-\delta (-1+t)$$

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

$$y^{\prime \prime }-7y^{\prime }+6y=\delta (-1+t)$$

$$y^{\prime \prime \prime }+y^{\prime \prime }+4y^{\prime }+4y=8$$

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

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

$$y^{\prime \prime \prime }-5y^{\prime \prime }+y^{\prime }-y=-t^2+2t-10$$

$$y^{\prime \prime \prime \prime }-5y^{\prime \prime }+4y=12\mathrm{Heaviside}\left(t\right)-12\mathrm{Heaviside}(-1+t)$$

$$y^{\prime \prime \prime \prime }-16y=32\mathrm{Heaviside}\left(t\right)-32\mathrm{Heaviside}(t-\pi )$$

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

$$y^{\prime \prime }-2y^{\prime }+5y={\mathrm{e}}^t$$

$$y^{\prime \prime }-3y^{\prime }-7y=4$$

$$y^{\prime \prime \prime }+3y^{\prime \prime }+3y^{\prime }+y=5$$

$$3y^{\prime \prime }+5y^{\prime }-2y=3t^2$$

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

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }=9y$$

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

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

$$y^{\prime \prime }+12y=7y^{\prime }$$

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

$$y^{\prime \prime }+2y^{\prime }+10y=0$$

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

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

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

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

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

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

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

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

$$y^{\prime \prime \prime \prime }-8y^{\prime \prime }+16y=0$$

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

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

$$y^{\prime \prime }-7y^{\prime }+12y=x$$

$$s^{\prime \prime }-a^{2}s=t+1$$

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

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

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

$$y^{\prime \prime }+6y^{\prime }+5y={\mathrm{e}}^{2x}$$

$$y^{\prime \prime }+9y=6{\mathrm{e}}^{3x}$$

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

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

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

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

$$y^{\prime \prime \prime \prime }-a^{4}y=5a^4{\mathrm{e}}^{ax}\sin \left(ax\right)$$

$$y^{\prime \prime \prime \prime }+2a^2{y}^{\prime \prime }+a^{4}y=8\cos \left(ax\right)$$

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

$$y^{\prime \prime }+n^{2}y=h\sin \left(rx\right)$$

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

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

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

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

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

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

$$y^{\prime \prime }-3y^{\prime }-10y=0$$

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

$$y^{\prime \prime \prime }-7y^{\prime \prime }+12y^{\prime }=0$$

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

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

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }-4y=31$$

$$y^{\prime \prime }+9y=27x+18$$

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

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

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

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

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

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

$$36y^{\prime \prime \prime \prime }-12y^{\prime \prime \prime }-11y^{\prime \prime }+2y^{\prime }+y=0$$

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

$$y^{\left(5\right)}-y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+35y^{\prime \prime }+16y^{\prime }-52y=0$$

$$y^{\left(8\right)}+8y^{\prime \prime \prime \prime }+16y=0$$

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

$$y^{\prime \prime \prime }+(-3-4i)y^{\prime \prime }+(-4+12i)y^{\prime }+12y=0$$

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

$$y^{\prime \prime \prime \prime }-6y^{\prime \prime \prime }+13y^{\prime \prime }-12y^{\prime }+4y=2{\mathrm{e}}^x-4{\mathrm{e}}^{2x}$$

$$y^{\prime \prime \prime \prime }+4y^{\prime \prime }=24x^2-6x+14+32\cos \left(2x\right)$$

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

$$y^{\prime \prime \prime \prime }-3y^{\prime \prime \prime }+3y^{\prime \prime }-y^{\prime }=6x-20-120{\mathrm{e}}^x{x}^2$$

$$y^{\prime \prime \prime }-6y^{\prime \prime }+21y^{\prime }-26y=36{\mathrm{e}}^{2x}\sin \left(3x\right)$$