What is the solution for x^{''}-(pi^2)x=-1/pi ?

The solution for x^{''}-(pi^2)x=-1/pi is x=c_{1}e^{pit}+c_{2}e^{-pit}+1/(pi^3)

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x^{''}-(pi^2)x=-1/pi

x^{^{''}} - (π^{2}) x = - \frac{1}{π}

x = c_{1} e^{π t} + c_{2} e^{- π t} + \frac{1}{π ^{3}}

Solution steps

x^{''} (t) - (π^{2}) x = - \frac{1}{π}

Solve linear ODE:

x = c_{1} e^{π t} + c_{2} e^{- π t} + \frac{1}{π ^{3}}

x = c_{1} e^{π t} + c_{2} e^{- π t} + \frac{1}{π ^{3}}

2 y^{^{''}} - 4 y^{^{'}} - 6 y = 16 e^{- x}

2 y^{^{''}} - 2 y^{^{'}} - 4 y = 2 e^{3} x

y^{^{''}} - 4 y^{^{'}} - 12 y = 12 t

y^{^{''}} - 2 y^{^{'}} + y = \frac{( e ^{t} )}{( 1 + t ^{2} ) + 3 e ^{t}}

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = x^{- 2} e^{x}

What is the solution for x^{''}-(pi^2)x=-1/pi ?
The solution for x^{''}-(pi^2)x=-1/pi is x=c_{1}e^{pit}+c_{2}e^{-pit}+1/(pi^3)