What is the solution for y^{''}-a*y+b=0 ?

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

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

y^{^{''}} - a \cdot y + b = 0

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 16 y^{^{'}} + 100 y = 10, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 4 y^{^{'}} + 3 y = cos (2 x)

y^{^{''}} + π^{2} y = \frac{5}{ln ( 10 )} sin (x ln (2))

\frac{d ^{2} y}{d t ^{2}} + 6 \frac{d y}{d t} + 9 y = e^{- 3 t}

y^{^{''}} + 2 y^{^{'}} + y = \frac{1}{x} e^{- x}

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