What is the solution for y^{''}+8y^'+15y=4 ?

The solution for y^{''}+8y^'+15y=4 is y=c_{1}e^{-3t}+c_{2}e^{-5t}+4/15

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y^{''}+8y^'+15y=4

y^{^{''}} + 8 y^{^{'}} + 15 y = 4

y = c_{1} e^{- 3 t} + c_{2} e^{- 5 t} + \frac{4}{15}

Solution steps

y^{''} (t) + 8 y^{'} (t) + 15 y = 4

Solve linear ODE:

y = c_{1} e^{- 3 t} + c_{2} e^{- 5 t} + \frac{4}{15}

y = c_{1} e^{- 3 t} + c_{2} e^{- 5 t} + \frac{4}{15}

y = \frac{4 x}{x ^{2} - 5}, (3, 3)

\int 4 e^{x} - \frac{5}{x} d x

5 x - x^{2}, 2 x, 0, 3

∣ x - 8 ∣, \frac{x}{3}

3 sin (2 t)

What is the solution for y^{''}+8y^'+15y=4 ?
The solution for y^{''}+8y^'+15y=4 is y=c_{1}e^{-3t}+c_{2}e^{-5t}+4/15