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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} + 5 y = 5 t

\frac{d ^{2} y}{d x ^{2}} + y = x

y^{^{''}} - 4 y = 4 x^{2} e^{2 x}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 9 y = \frac{1}{( cos ( 3 x ) )}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 25 y = 2

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