What is the solution for y^{''}-2y^'+26y=e^xsin(x) ?

The solution for y^{''}-2y^'+26y=e^xsin(x) is y=e^x(c_{1}cos(5x)+c_{2}sin(5x))+1/24 e^xsin(x)

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y^{''}-2y^'+26y=e^xsin(x)

y^{^{''}} - 2 y^{^{'}} + 26 y = e^{x} sin (x)

y = e^{x} (c_{1} cos (5 x) + c_{2} sin (5 x)) + \frac{1}{24} e^{x} sin (x)

Solution steps

y^{''} (x) - 2 y^{'} (x) + 26 y = e^{x} sin (x)

Solve linear ODE:

y = e^{x} (c_{1} cos (5 x) + c_{2} sin (5 x)) + \frac{1}{24} e^{x} sin (x)

y = e^{x} (c_{1} cos (5 x) + c_{2} sin (5 x)) + \frac{1}{24} e^{x} sin (x)

What is the solution for y^{''}-2y^'+26y=e^xsin(x) ?
The solution for y^{''}-2y^'+26y=e^xsin(x) is y=e^x(c_{1}cos(5x)+c_{2}sin(5x))+1/24 e^xsin(x)