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

The solution for (d^2y)/(dx^2)-2(dy)/(dx)-3y=2e^{4x} is y=c_{1}e^{3x}+c_{2}e^{-x}+2/5 e^{4x}

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + y^{^{'}} = sec (x) tan (x)

y^{^{''}} + 4 y = t^{2} + 7 e^{t}

y^{^{''''}} - 8 y^{^{''}} + 16 y = x^{2}

d (x) = \frac{100}{π} e^{- 100 x^{2} (x)^{2}}

y^{^{''}} - y^{^{'}} = x e (x), y (0) = 2, y^{^{'}} (0) = 1

What is the solution for (d^2y)/(dx^2)-2(dy)/(dx)-3y=2e^{4x} ?
The solution for (d^2y)/(dx^2)-2(dy)/(dx)-3y=2e^{4x} is y=c_{1}e^{3x}+c_{2}e^{-x}+2/5 e^{4x}