What is the solution for -ay^{''}+by-1=0 ?

The solution for -ay^{''}+by-1=0 is y=c_{1}e^{sqrt(b/a)t}+c_{2}e^{-sqrt(b/a)t}+1/b

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-ay^{''}+by-1=0

- a y^{^{''}} + b y - 1 = 0

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

Solution steps

- a y^{''} (t) + b y - 1 = 0

Solve linear ODE:

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

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

What is the solution for -ay^{''}+by-1=0 ?
The solution for -ay^{''}+by-1=0 is y=c_{1}e^{sqrt(b/a)t}+c_{2}e^{-sqrt(b/a)t}+1/b