What is the solution for (d^2y)/(dx^2)-2(dy)/(dx)-3y=4e^x-9 ?

The solution for (d^2y)/(dx^2)-2(dy)/(dx)-3y=4e^x-9 is y=c_{1}e^{3x}+c_{2}e^{-x}-e^x+3

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(d^2y)/(dx^2)-2(dy)/(dx)-3y=4e^x-9

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} - 3 y = 4 e^{x} - 9

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} - 3 y = 4 e^{x} - 9

Solve linear ODE:

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

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

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = cos (2 x)

x^{^{''}} + 2 x = cos (8 t)

y^{^{''}} + 12 y^{^{'}} + 37 = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{''}} - y^{^{'}} = 2 t^{2} + t - 1

y^{^{''}} - 2 y = 12 x - 10

What is the solution for (d^2y)/(dx^2)-2(dy)/(dx)-3y=4e^x-9 ?
The solution for (d^2y)/(dx^2)-2(dy)/(dx)-3y=4e^x-9 is y=c_{1}e^{3x}+c_{2}e^{-x}-e^x+3