What is the solution for (d^2v)/(dx^2)-k^2v=k^2n ?

The solution for (d^2v)/(dx^2)-k^2v=k^2n is v=c_{1}e^{kx}+c_{2}e^{-kx}-n

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(d^2v)/(dx^2)-k^2v=k^2n

\frac{d ^{2} v}{d x ^{2}} - k^{2} v = k^{2} n

v = c_{1} e^{k x} + c_{2} e^{- k x} - n

Solution steps

\frac{d ^{2} v}{d x ^{2}} - k^{2} v = k^{2} n

Solve linear ODE:

v = c_{1} e^{k x} + c_{2} e^{- k x} - n

v = c_{1} e^{k x} + c_{2} e^{- k x} - n

y^{^{'''}} + 12 y^{^{''}} + 48 y^{^{'}} + 64 y = 9 e^{- 4 x}

y^{^{''}} + 3 y^{^{'}} + 2 y = 5 e^{- 2 x}

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - y = 12

y^{^{''}} + 36 y = 33 cos (5 t)

y^{^{''}} + 4 y = 5 (e^{x} + e^{3 x})

What is the solution for (d^2v)/(dx^2)-k^2v=k^2n ?
The solution for (d^2v)/(dx^2)-k^2v=k^2n is v=c_{1}e^{kx}+c_{2}e^{-kx}-n