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

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

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

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

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

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

$$y^{\prime \prime }+4y=t-\frac{1}{20}{t}^2$$

$$y^{\prime \prime }+5y^{\prime }+6y=4+{\mathrm{e}}^{-t}$$

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

$$y^{\prime \prime }+6y^{\prime }+8y=2t+{\mathrm{e}}^{-t}$$

$$y^{\prime \prime }+6y^{\prime }+8y=2t+{\mathrm{e}}^t$$

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

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

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

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

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

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

$$y^{\prime \prime }+6y^{\prime }+8y=\cos \left(t\right)$$

$$y^{\prime \prime }+6y^{\prime }+8y=-4\cos \left(3t\right)$$

$$y^{\prime \prime }+4y^{\prime }+13y=3\cos \left(2t\right)$$

$$y^{\prime \prime }+4y^{\prime }+20y=-\cos \left(5t\right)$$

$$y^{\prime \prime }+4y^{\prime }+20y=-3\sin \left(2t\right)$$

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

$$y^{\prime \prime }+6y^{\prime }+8y=\cos \left(t\right)$$

$$y^{\prime \prime }+6y^{\prime }+8y=2\cos \left(3t\right)$$

$$y^{\prime \prime }+6y^{\prime }+20y=-3\sin \left(2t\right)$$

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

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

$$y^{\prime \prime }+4y^{\prime }+20y=3+2\cos \left(2t\right)$$

$$y^{\prime \prime }+4y^{\prime }+20y={\mathrm{e}}^{-t}\cos \left(t\right)$$

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

$$y^{\prime \prime }+9y=5\sin \left(2t\right)$$

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

$$y^{\prime \prime }+4y=3\cos \left(2t\right)$$

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

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

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

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

$$y^{\prime \prime }+6y^{\prime }+13y=13\mathrm{Heaviside}(t-4)$$

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

$$y^{\prime \prime }+3y=\mathrm{Heaviside}(t-4)\cos (5t-20)$$

$$y^{\prime \prime }+4y^{\prime }+9y=20\mathrm{Heaviside}(t-2)\sin (t-2)$$

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

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

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

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

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

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

$$y^{\prime \prime }+y^{\prime }+5y=\mathrm{Heaviside}(t-2)\sin (4t-8)$$

$$y^{\prime \prime }+y^{\prime }+8y=(1-\mathrm{Heaviside}(t-4))\cos (t-4)$$

$$y^{\prime \prime }+y^{\prime }+3y=(1-\mathrm{Heaviside}(t-2)){\mathrm{e}}^{-\frac{t}{10}+\frac{1}{5}}\sin (t-2)$$

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

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

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

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

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

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

$$y^{\prime \prime }+3y^{\prime }+8y={\mathrm{e}}^{-x^2}$$

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

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

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

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

$$x{y}^{\prime \prime }+4y^{\prime }=18x^2$$

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

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

$$y^{\prime \prime }+2y^{\prime }=8{\mathrm{e}}^{2x}$$

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

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

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

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

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

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

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

$$x{y}^{\prime \prime }+4y^{\prime }=18x^2$$

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

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

$$y^{\prime \prime }+2y^{\prime }=8{\mathrm{e}}^{2x}$$

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

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

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

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

$$y^{\prime \prime }=2y^{\prime }-5y+30{\mathrm{e}}^{3x}$$

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

$$y^{\prime \prime }-10y^{\prime }+25y=0$$

$$x^2{y}^{\prime \prime }-6x{y}^{\prime }+12y=0$$

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

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

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

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }-6y^{\prime }+8y={\mathrm{e}}^{4x}$$

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

$$x^2{y}^{\prime \prime }-20y=27x^5$$