What is the solution for (d^2y)/(dx^2)+3(dy)/(dx)+2y=e^{4x} ?

The solution for (d^2y)/(dx^2)+3(dy)/(dx)+2y=e^{4x} is y=c_{1}e^{-x}+c_{2}e^{-2x}+1/30 e^{4x}

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(d^2y)/(dx^2)+3(dy)/(dx)+2y=e^{4x}

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} + 2 y = e^{4 x}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{1}{30} e^{4 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} + 2 y = e^{4 x}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{1}{30} e^{4 x}

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + \frac{1}{30} e^{4 x}

y^{^{''}} - 4 y^{^{'}} - 3 y = cos (2 x)

y^{^{''}} + 4 y^{^{'}} = - 32 (x + 2), y (0) = 0, y^{^{'}} (0) = - 10

3 y^{^{''}} - 4 y^{^{'}} - 5 y = (x^{2} + 1) e^{- x}

y^{^{''}} + k^{2} y = k sin (k x)

2 y^{^{''}} + y^{^{'}} + 1 = 2 e^{2} x

What is the solution for (d^2y)/(dx^2)+3(dy)/(dx)+2y=e^{4x} ?
The solution for (d^2y)/(dx^2)+3(dy)/(dx)+2y=e^{4x} is y=c_{1}e^{-x}+c_{2}e^{-2x}+1/30 e^{4x}