What is the solution for y^{''}-6y=9t ?

The solution for y^{''}-6y=9t is y=c_{1}e^{sqrt(6)t}+c_{2}e^{-sqrt(6)t}-(3t)/2

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y^{''}-6y=9t

y^{^{''}} - 6 y = 9 t

y = c_{1} e^{6 t} + c_{2} e^{- 6 t} - \frac{3 t}{2}

Solution steps

y^{''} (t) - 6 y = 9 t

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} e^{- 6 t} - \frac{3 t}{2}

y = c_{1} e^{6 t} + c_{2} e^{- 6 t} - \frac{3 t}{2}

\int 5 x^{2} + 9 d x

t v^{^{'}} (1 - t^{2}) + 2 v = 0

\int x (x^{2} - 1)^{2} d x

(1 + x)^{n}

f (x) = - \frac{12}{( x - 6 ) ^{2}}

What is the solution for y^{''}-6y=9t ?
The solution for y^{''}-6y=9t is y=c_{1}e^{sqrt(6)t}+c_{2}e^{-sqrt(6)t}-(3t)/2