What is the solution for (D^2+2D-3)y=cos(2x) ?

The solution for (D^2+2D-3)y=cos(2x) is y=c_{1}e^x+c_{2}e^{-3x}+4/65 sin(2x)-7/65 cos(2x)

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(D^2+2D-3)y=cos(2x)

(D^{2} + 2 D - 3) y = cos (2 x)

y = c_{1} e^{x} + c_{2} e^{- 3 x} + \frac{4}{65} sin (2 x) - \frac{7}{65} cos (2 x)

Solution steps

(D^{2} + 2 D - 3) y = cos (2 x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 3 x} + \frac{4}{65} sin (2 x) - \frac{7}{65} cos (2 x)

y = c_{1} e^{x} + c_{2} e^{- 3 x} + \frac{4}{65} sin (2 x) - \frac{7}{65} cos (2 x)

What is the solution for (D^2+2D-3)y=cos(2x) ?
The solution for (D^2+2D-3)y=cos(2x) is y=c_{1}e^x+c_{2}e^{-3x}+4/65 sin(2x)-7/65 cos(2x)