What is the solution for (d^2y)/(dx^2)-49y=e^{7x} ?

The solution for (d^2y)/(dx^2)-49y=e^{7x} is y=c_{1}e^{7x}+c_{2}e^{-7x}+(e^{7x}x)/(14)

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(d^2y)/(dx^2)-49y=e^{7x}

\frac{d ^{2} y}{d x ^{2}} - 49 y = e^{7 x}

y = c_{1} e^{7 x} + c_{2} e^{- 7 x} + \frac{e ^{7 x} x}{14}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 49 y = e^{7 x}

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} e^{- 7 x} + \frac{e ^{7 x} x}{14}

y = c_{1} e^{7 x} + c_{2} e^{- 7 x} + \frac{e ^{7 x} x}{14}

\int \frac{x}{8 - 2 x ^{2} - x ^{4}} d x

\int sin (7 x) d x

y^{^{''}} + 4 y = 4 t

What is the solution for (d^2y)/(dx^2)-49y=e^{7x} ?
The solution for (d^2y)/(dx^2)-49y=e^{7x} is y=c_{1}e^{7x}+c_{2}e^{-7x}+(e^{7x}x)/(14)