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

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

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

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

$$x^{\prime \prime }=-3\sqrt{t}$$

$$x^{\prime \prime }+x^{\prime }=3t$$

$$x^{\prime \prime }+x^{\prime }+x=3t^3-1$$

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

$$x^{\prime \prime }+x^{\prime }+x=12$$

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

$$x^{\prime \prime }+x^{\prime }+x=5\sin \left(7t\right)$$

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

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

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

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

$$x^{\prime \prime }+x^{\prime }+x=5\sin \left(2t\right)+t{\mathrm{e}}^t$$

$$x^{\prime \prime }+x^{\prime }+x=t^3+1-4t\cos \left(t\right)$$

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

$$x^{\prime \prime }+7x=t{\mathrm{e}}^{3t}$$

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

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

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

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

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

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

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

$$x^{\prime \prime }-3x^{\prime }-40x=2{\mathrm{e}}^{-t}$$

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

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

$$x^{\prime \prime }+\frac{x^{\prime }}{100}+4x=\cos \left(2t\right)$$

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

$$x^{\prime \prime }+3025x=\cos \left(45t\right)$$

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

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

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

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

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

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

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

$$x^{\prime \prime }+\frac{2x^{\prime }}{5}+2x=1-\mathrm{Heaviside}(t-5)$$

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

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

$$x^{\prime \prime }+{\pi }^{2}x={\pi }^2\mathrm{Heaviside}(1-t)$$

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

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

$$x^{\prime \prime }-x=\delta (t-5)$$

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

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

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

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

$$x^{\prime \prime }+4x=\frac{\mathrm{Heaviside}(t-5)(t-5)}{5}+(2-\frac{t}{5})\mathrm{Heaviside}(t-10)$$

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

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

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

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

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

$$y^{\prime \prime }-5y^{\prime }+6y=2-12x+6{\mathrm{e}}^x$$

$$y^{\prime \prime }-3y^{\prime }+8y=4x^2$$

$$y^{\prime \prime }-2y^{\prime }-8y=4{\mathrm{e}}^{2x}-21{\mathrm{e}}^{-3x}$$

$$y^{\prime \prime }+2y^{\prime }+5y=6\sin \left(2x\right)+7\cos \left(2x\right)$$

$$y^{\prime \prime }+2y^{\prime }+2y=10\sin \left(4x\right)$$

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

$$y^{\prime \prime }-3y^{\prime }-4y=16x-12{\mathrm{e}}^{2x}$$

$$y^{\prime \prime }+6y^{\prime }+5y=2{\mathrm{e}}^x+10{\mathrm{e}}^{5x}$$

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

$$y^{\prime \prime }+y^{\prime }-6y=10{\mathrm{e}}^{2x}-18{\mathrm{e}}^{3x}-6x-11$$

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

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

$$y^{\prime \prime }+4y=12x^2-16x\cos \left(2x\right)$$

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

$$y^{\prime \prime }+5y^{\prime }+4y=16x+20{\mathrm{e}}^x$$

$$y^{\prime \prime }-8y^{\prime }+15y=9{\mathrm{e}}^{2x}x$$

$$y^{\prime \prime }+7y^{\prime }+10y=4x{\mathrm{e}}^{-3x}$$

$$y^{\prime \prime }+8y^{\prime }+16y=8{\mathrm{e}}^{-2x}$$

$$y^{\prime \prime }+6y^{\prime }+9y=27{\mathrm{e}}^{-6x}$$

$$y^{\prime \prime }+4y^{\prime }+13y=18{\mathrm{e}}^{-2x}$$

$$y^{\prime \prime }-10y^{\prime }+29y=8{\mathrm{e}}^{5x}$$

$$y^{\prime \prime }-4y^{\prime }+13y=8\sin \left(3x\right)$$

$$y^{\prime \prime }-y^{\prime }-6y=8{\mathrm{e}}^{2x}-5{\mathrm{e}}^{3x}$$

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

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

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

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

$$y^{\prime \prime }-6y^{\prime }+8y=x^3+x+{\mathrm{e}}^{-2x}$$

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

$$y^{\prime \prime }+4y^{\prime }+5y={\mathrm{e}}^{-2x}(\cos \left(x\right)+1)$$

$$y^{\prime \prime }-6y^{\prime }+9y=x^4{\mathrm{e}}^x+x^3{\mathrm{e}}^{2x}+x^2{\mathrm{e}}^{3x}$$

$$y^{\prime \prime }+6y^{\prime }+13y=x{\mathrm{e}}^{-3x}\sin \left(2x\right)+x^2{\mathrm{e}}^{-2x}\sin \left(3x\right)$$

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

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

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

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

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

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

$$y^{\prime \prime }+4y^{\prime }+5y={\mathrm{e}}^{-2x}\sec \left(x\right)$$

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

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

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

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

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