What is the solution for y^{''}-2y^{''}-3y=4e^x-9 ?

The solution for y^{''}-2y^{''}-3y=4e^x-9 is y=c_{1}cos(sqrt(3)x)+c_{2}sin(sqrt(3)x)-e^x+3

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y^{''}-2y^{''}-3y=4e^x-9

y^{^{''}} - 2 y^{^{''}} - 3 y = 4 e^{x} - 9

y = c_{1} cos (3 x) + c_{2} sin (3 x) - e^{x} + 3

Solution steps

y^{''} (x) - 2 y^{''} (x) - 3 y = 4 e^{x} - 9

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) - e^{x} + 3

y = c_{1} cos (3 x) + c_{2} sin (3 x) - e^{x} + 3

((d^{2}) - 1) y = x sin (x) + (1 + x^{2}) e^{x}

y^{^{''}} - 5 y^{^{'}} + 6 y = g (x)

y^{^{''}} - 12 y^{^{'}} + 35 y = 96 e^{t}

y^{^{''}} + y + 2 sin (x) = 0

y^{^{''}} - 2 y^{^{'}} + y = 2 sin (t), y^{^{'}} (0) = 2, y (0) = 1

What is the solution for y^{''}-2y^{''}-3y=4e^x-9 ?
The solution for y^{''}-2y^{''}-3y=4e^x-9 is y=c_{1}cos(sqrt(3)x)+c_{2}sin(sqrt(3)x)-e^x+3