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Popular Calculus >

y^{''}-3y^'+2y=e^xsin(2x)

Solution

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

Solution

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{1}{10} e^{x} cos (2 x) - \frac{1}{5} e^{x} sin (2 x)

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{1}{10} e^{x} cos (2 x) - \frac{1}{5} e^{x} sin (2 x)

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{1}{10} e^{x} cos (2 x) - \frac{1}{5} e^{x} sin (2 x)

Graph

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Frequently Asked Questions (FAQ)

What is the solution for y^{''}-3y^'+2y=e^xsin(2x) ?
The solution for y^{''}-3y^'+2y=e^xsin(2x) is y=c_{1}e^{2x}+c_{2}e^x+1/10 e^xcos(2x)-1/5 e^xsin(2x)