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Popular >

y^{''}-5y^'+6y=cos(2x)+1

Solution

y^{^{''}} - 5 y^{^{'}} + 6 y = cos (2 x) + 1

Solution

y = c_{1} e^{3 x} + c_{2} e^{2 x} + e^{3 x} (- \frac{2}{3} e^{- 3 x} cos^{2} (x) + \frac{4}{39} e^{- 3 x} cos (2 x) + \frac{2}{13} e^{- 3 x} sin (2 x)) + e^{2 x} \cdot \int - \frac{2 cos ^{2} ( x )}{e ^{2 x}} d x

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 y = cos (2 x) + 1

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + e^{3 x} (- \frac{2}{3} e^{- 3 x} cos^{2} (x) + \frac{4}{39} e^{- 3 x} cos (2 x) + \frac{2}{13} e^{- 3 x} sin (2 x)) + e^{2 x} \cdot \int - \frac{2 cos ^{2} ( x )}{e ^{2 x}} d x

y = c_{1} e^{3 x} + c_{2} e^{2 x} + e^{3 x} (- \frac{2}{3} e^{- 3 x} cos^{2} (x) + \frac{4}{39} e^{- 3 x} cos (2 x) + \frac{2}{13} e^{- 3 x} sin (2 x)) + e^{2 x} \cdot \int - \frac{2 cos ^{2} ( x )}{e ^{2 x}} d x

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