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

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

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

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

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

$$y^{\prime \prime }+4y^{\prime }+5y=6\sin \left(t\right)$$

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

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

$$y^{\prime \prime }+6y^{\prime }+10y=50x$$

$$x^{\prime \prime }+2x^{\prime }+2x=85\sin \left(3t\right)$$

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

$$x^{\prime \prime }+5x^{\prime }+6x=\cos \left(t\right)$$

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

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

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

$$y^{\prime \prime }-6y^{\prime }+25y=2\sin \left(\frac{t}{2}\right)-\cos \left(\frac{t}{2}\right)$$

$$y^{\prime \prime }-6y^{\prime }+25y=64{\mathrm{e}}^{-t}$$

$$y^{\prime \prime }-6y^{\prime }+25y=50t^3-36t^2-63t+18$$

$$y^{\prime \prime }=9x^2+2x-1$$

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

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

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

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }-60y^{\prime }-900y=5{\mathrm{e}}^{10x}$$

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

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

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

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

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

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

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

$$q^{\prime \prime }+9q^{\prime }+14q=\frac{\sin \left(t\right)}{2}$$

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

$$y^{\prime \prime }-3y^{\prime }+2y=2(1-x){\mathrm{e}}^x$$

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

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

$$y^{\prime \prime }-4y^{\prime }+3y=1$$

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

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }-4y^{\prime }+3y=\frac{1}{1+{\mathrm{e}}^{-x}}$$

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

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

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }+5y=\cos \left(x\sqrt{5}\right)$$

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

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

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

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

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

$$y^{\prime \prime }+5y^{\prime }+6y={\mathrm{e}}^{-2x}\sec {\left(x\right)}^2(1+2\tan \left(x\right))$$

$$y^{\prime \prime }+9y=10{\mathrm{e}}^{-t}$$

$$y^{\prime \prime }-6y^{\prime }+5y=29\cos \left(2t\right)$$

$$y^{\prime \prime }+7y^{\prime }+12y=21{\mathrm{e}}^{3t}$$

$$y^{\prime \prime }-4y^{\prime }+3y=6t-8$$

$$y^{\prime \prime }+\frac{y}{25}=\frac{t^2}{50}$$

$$y^{\prime \prime }+3y^{\prime }+\frac{9y}{4}=9t^3+64$$

$$y^{\prime \prime }+2y^{\prime }+5y=50t-100$$

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

$$y^{\prime \prime }+6y^{\prime }+8y={\mathrm{e}}^{-3t}-{\mathrm{e}}^{-5t}$$

$$y^{\prime \prime }+10y^{\prime }+24y=144t^2$$

\[ {}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 8 \sin \left (t \right ) & 0

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 4 t & 0

\[ {}y^{\prime \prime }+y^{\prime }-2 y = \left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0

\[ {}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0

\[ {}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 8 t^{2} & 0

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

$$y^{\prime \prime }+16y=4\delta (t-3\pi )$$

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

$$y^{\prime \prime }+4y^{\prime }+5y=\delta (-1+t)$$

$$4y^{\prime \prime }+24y^{\prime }+37y=17{\mathrm{e}}^{-t}+\delta (t-\frac{1}{2})$$

$$y^{\prime \prime }+3y^{\prime }+2y=10\sin \left(t\right)+10\delta (-1+t)$$

$$y^{\prime \prime }+4y^{\prime }+5y=(1-\mathrm{Heaviside}(t-10)){\mathrm{e}}^t-{\mathrm{e}}^{10}\delta (t-10)$$

$$y^{\prime \prime }+5y^{\prime }+6y=\delta (t-\frac{\pi }{2})+\mathrm{Heaviside}(t-\pi )\cos \left(t\right)$$

$$y^{\prime \prime }+5y^{\prime }+6y=\mathrm{Heaviside}(-1+t)+\delta (t-2)$$