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

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

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

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

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

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

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

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

$${(2x+1)}^2{y}^{\prime \prime }-2(2x+1)y^{\prime }-12y=6x$$

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

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

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

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

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

$$x^4{y}^{\prime \prime }+2x^3{y}^{\prime }+y=\frac{1+x}{x}$$

$$x^8{y}^{\prime \prime }+4x^7{y}^{\prime }+y=\frac{1}{x^3}$$

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

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

$$(1+x)y^{\prime \prime }-(3x+4)y^{\prime }+3y=(2+3x){\mathrm{e}}^{3x}$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}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

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }+2y^{\prime }+5y=25t-100\delta (t-\pi )$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$p{x}^2{u}^{\prime \prime }+qx{u}^{\prime }+ru=f\left(x\right)$$

$$y^{\prime \prime }+6y^{\prime }+9y=50{\mathrm{e}}^{2x}$$

$$y^{\prime \prime }-4y^{\prime }+4y=50{\mathrm{e}}^{2x}$$

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

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

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

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

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

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

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

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

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

$$y^{\prime \prime }-4y^{\prime }+5y=3{\mathrm{e}}^{-x}+2x^2$$

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

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

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

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

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

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

$$y^{\prime \prime }-2i{y}^{\prime }-y={\mathrm{e}}^{ix}-2{\mathrm{e}}^{-ix}$$

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

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

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

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

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

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

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

$$x^2{y}^{\prime \prime }-5x{y}^{\prime }+9y=x^2$$

$$x^2{y}^{\prime \prime }+x{y}^{\prime }+4y=1$$

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

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

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

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