What is the solution for y^{''}+9y=13e^{2x}+10sin(2x) ?

The solution for y^{''}+9y=13e^{2x}+10sin(2x) is y=c_{1}cos(3x)+c_{2}sin(3x)+e^{2x}+2sin(2x)

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y^{''}+9y=13e^{2x}+10sin(2x)

y^{^{''}} + 9 y = 13 e^{2 x} + 10 sin (2 x)

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

Solution steps

y^{''} (x) + 9 y = 13 e^{2 x} + 10 sin (2 x)

Solve linear ODE:

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

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

y^{^{''}} - 3 y^{^{'}} = sin (2 x)

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

y^{^{''}} + 4 y^{^{'}} + 3 y = 1

y^{^{''}} + 4 y = 9 sin (t), y (0) = 1, y^{^{'}} (0) = - 1

y^{^{''}} + y^{^{'}} = 2 e^{x}

What is the solution for y^{''}+9y=13e^{2x}+10sin(2x) ?
The solution for y^{''}+9y=13e^{2x}+10sin(2x) is y=c_{1}cos(3x)+c_{2}sin(3x)+e^{2x}+2sin(2x)