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

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

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

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

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

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

$$x^{\prime \prime }-4x=t^2$$

$$x^{\prime \prime }-4x^{\prime }=t^2$$

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

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

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

$$x^{\prime \prime }+{\omega }^{2}x=\sin \left(\alpha t\right)$$

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

$$x^{\prime \prime }+2x^{\prime }+10x={\mathrm{e}}^{-t}$$

$$x^{\prime \prime }+2x^{\prime }+10x={\mathrm{e}}^{-t}\cos \left(3t\right)$$

$$x^{\prime \prime }+6x^{\prime }+10x={\mathrm{e}}^{-2t}\cos \left(t\right)$$

$$x^{\prime \prime }+4x^{\prime }+4x={\mathrm{e}}^{2t}$$

$$x^{\prime \prime }+x^{\prime }-2x=12{\mathrm{e}}^{-t}-6{\mathrm{e}}^t$$

$$x^{\prime \prime }+4x=289t{\mathrm{e}}^t\sin \left(2t\right)$$

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

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

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

$$x^{\prime \prime }-x=\frac{1}{t}$$

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

$$x^{\prime \prime }-4x^{\prime }=\tan \left(t\right)$$

$$y^{\prime \prime }-6y^{\prime }+10y=100$$

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

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

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

$$x^{\prime \prime }-4x^{\prime }+4x={\mathrm{e}}^t+{\mathrm{e}}^{2t}+1$$

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

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

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

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

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

$$x^{\prime \prime }+10x^{\prime }+25x=2^t+t{\mathrm{e}}^{-5t}$$

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

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

$$y^{\prime \prime }+2y^{\prime }+3y=9t$$

$$4y^{\prime \prime }+16y^{\prime }+17y=17t-1$$

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

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

$$y^{\prime \prime }+9y={\mathrm{e}}^{-2t}$$

$$2y^{\prime \prime }-3y^{\prime }+17y=17t-1$$

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

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

$$y^{\prime \prime }+8y^{\prime }+20y=\sin \left(2t\right)$$

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

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

$$3y^{\prime \prime }+5y^{\prime }-2y=7{\mathrm{e}}^{-2t}$$

$$y^{\prime \prime }+9y=24\sin \left(t\right)(\mathrm{Heaviside}\left(t\right)+\mathrm{Heaviside}(t-\pi ))$$

$$y^{\prime \prime }+2y^{\prime }+y=\mathrm{Heaviside}\left(t\right)-\mathrm{Heaviside}(-1+t)$$

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

$$y^{\prime \prime }+5y^{\prime }+6y=36t(\mathrm{Heaviside}\left(t\right)-\mathrm{Heaviside}(-1+t))$$

$$y^{\prime \prime }+4y^{\prime }+13y=39\mathrm{Heaviside}\left(t\right)-507(t-2)\mathrm{Heaviside}(t-2)$$

$$y^{\prime \prime }+4y=3\mathrm{Heaviside}\left(t\right)-3\mathrm{Heaviside}(t-4)+(2t-5)\mathrm{Heaviside}(t-4)$$

$$4y^{\prime \prime }+4y^{\prime }+5y=25t(\mathrm{Heaviside}\left(t\right)-\mathrm{Heaviside}(t-\frac{\pi }{2}))$$

$$y^{\prime \prime }+4y^{\prime }+3y=\mathrm{Heaviside}\left(t\right)-\mathrm{Heaviside}(-1+t)+\mathrm{Heaviside}(t-2)-\mathrm{Heaviside}(t-3)$$

$$y^{\prime \prime }-2y^{\prime }=\{\begin{array}{cc}4& 0\le t<1\\ 6& 1\le t\end{array}$$

$$y^{\prime \prime }-3y^{\prime }+2y=\{\begin{array}{cc}0& 0\le t<1\\ 1& 1\le t<2\\ -1& 2\le t\end{array}$$

$$y^{\prime \prime }+3y^{\prime }+2y=\{\begin{array}{cc}1& 0\le t<2\\ -1& 2\le t\end{array}$$

$$y^{\prime \prime }+y=\{\begin{array}{cc}t& 0\le t<\pi \\ -t& \pi \le t\end{array}$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }-9y=2\sin \left(3x\right)$$

$$y^{\prime \prime }+9y=2\sin \left(3x\right)$$

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

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