What is the solution for 2(d^2y)/(dx^2)-4(dy)/(dx)-6y=3e^{2x} ?

The solution for 2(d^2y)/(dx^2)-4(dy)/(dx)-6y=3e^{2x} is y=c_{1}e^{3x}+c_{2}e^{-x}-1/2 e^{2x}

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2(d^2y)/(dx^2)-4(dy)/(dx)-6y=3e^{2x}

2 \frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 6 y = 3 e^{2 x}

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

Solution steps

2 \frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 6 y = 3 e^{2 x}

Solve linear ODE:

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

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

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

y^{^{''}} + 12 y^{^{'}} + 27 y = 64 e^{- 1 t}, y (0) = 5

y^{^{''}} - y = e^{t} sin (t)

y^{^{''}} + 3 y^{^{'}} - 4 y = 3 e^{2} x

y^{^{''}} - 2 y^{^{'}} - 3 y = e^{x}

What is the solution for 2(d^2y)/(dx^2)-4(dy)/(dx)-6y=3e^{2x} ?
The solution for 2(d^2y)/(dx^2)-4(dy)/(dx)-6y=3e^{2x} is y=c_{1}e^{3x}+c_{2}e^{-x}-1/2 e^{2x}