What is the solution for (d^2y)/(dx^2)-a^2y+b=0 ?

The solution for (d^2y)/(dx^2)-a^2y+b=0 is y=c_{1}e^{ax}+c_{2}e^{-ax}+b/(a^2)

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(d^2y)/(dx^2)-a^2y+b=0

\frac{d ^{2} y}{d x ^{2}} - a^{2} y + b = 0

y = c_{1} e^{a x} + c_{2} e^{- a x} + \frac{b}{a ^{2}}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - a^{2} y + b = 0

Solve linear ODE:

y = c_{1} e^{a x} + c_{2} e^{- a x} + \frac{b}{a ^{2}}

y = c_{1} e^{a x} + c_{2} e^{- a x} + \frac{b}{a ^{2}}

What is the solution for (d^2y)/(dx^2)-a^2y+b=0 ?
The solution for (d^2y)/(dx^2)-a^2y+b=0 is y=c_{1}e^{ax}+c_{2}e^{-ax}+b/(a^2)