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

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

$$y^{\prime \prime }-2y^{\prime }+5y=t+1$$

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

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

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

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

$$y^{\prime \prime }+4y^{\prime }+3y=1-\mathrm{Heaviside}(t-2)-\mathrm{Heaviside}(t-4)+\mathrm{Heaviside}(t-6)$$

$$y^{\prime \prime }+9y=\cos \left(3t\right)$$

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

$$y^{\prime \prime }+16y=\{\begin{array}{cc}\cos \left(4t\right)& 0\le t<\pi \\ 0& \pi \le t\end{array}$$

$$y^{\prime \prime }+y=\{\begin{array}{cc}1& 0\le t<\frac{\pi }{2}\\ \sin \left(t\right)& \frac{\pi }{2}\le t\end{array}$$

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

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

$$y^{\prime \prime }+16y=\delta (t-2\pi )$$

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

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

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

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

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

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

$$y^{\prime \prime }+4y^{\prime }+13y=\delta (t-\pi )+\delta (t-3\pi )$$

$$y^{\prime \prime }-7y^{\prime }+6y={\mathrm{e}}^t+\delta (t-2)+\delta (t-4)$$

$$y^{\prime \prime }+2y^{\prime }+10y=\delta \left(t\right)$$

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

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

$$y^{\prime \prime }+3y^{\prime }+2y=12x^2$$

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

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

$$y^{\prime \prime }+16y=4\cos \left(x\right)$$

$$y^{\prime \prime }-4y^{\prime }+3y=9x^2+4$$

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

$$y^{\prime \prime }+y^{\prime }+4y=1$$

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

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

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

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

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

$$z^{\prime \prime }+3z^{\prime }+2z=24{\mathrm{e}}^{-3t}-24{\mathrm{e}}^{-4t}$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }-5y^{\prime }+6y=\cos \left(x\right)-{\mathrm{e}}^{2x}$$

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