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

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y^{''}-a(y+b)=0

y^{^{''}} - a (y + b) = 0

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

Solution steps

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

Solve linear ODE:

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

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

f (x) = x^{3} + e^{4 x} x^{2}

\int \frac{1}{x ^{2} - 6 x + 10} d x

\frac{d}{d x} (x^{3} + (3 - 3 x^{2})^{2} + 4)

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

x \to 2 lim (sin (\frac{π x}{2}))

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