What is the solution for (d^2y)/(dx^2)+(dy)/(dx)-6y=36x ?

The solution for (d^2y)/(dx^2)+(dy)/(dx)-6y=36x is y=c_{1}e^{2x}+c_{2}e^{-3x}-6x-1

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(d^2y)/(dx^2)+(dy)/(dx)-6y=36x

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 6 y = 36 x

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - 6 x - 1

Solution steps

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 6 y = 36 x

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - 6 x - 1

y = c_{1} e^{2 x} + c_{2} e^{- 3 x} - 6 x - 1

y = 1 + t - 1 - t

n = 1 \sum \infty \frac{2}{1 0 ^{n}}

\int (\frac{x + 6}{x}) d x

\frac{d}{d x} (\frac{2 x + x ^{4}}{( 1 - x ^{3} ) ^{2}})

\int ln (sin (x)) d x

What is the solution for (d^2y)/(dx^2)+(dy)/(dx)-6y=36x ?
The solution for (d^2y)/(dx^2)+(dy)/(dx)-6y=36x is y=c_{1}e^{2x}+c_{2}e^{-3x}-6x-1