y^{''}-2y^'+17y=excos(4x)

Lösung

y^{^{''}} - 2 y^{^{'}} + 17 y = e x cos (4 x)

y = e^{x} (c_{1} cos (4 x) + c_{2} sin (4 x)) - \frac{8 e x sin ( 4 x )}{65} + \frac{e x cos ( 4 x )}{65} - \frac{536 e}{4225} sin (4 x) + \frac{2 e}{4225} cos (4 x)

Schritte zur Lösung

y^{''} (x) - 2 y^{'} (x) + 17 y = e x cos (4 x)

Solve linear ODE:

y = e^{x} (c_{1} cos (4 x) + c_{2} sin (4 x)) - \frac{8 e x sin ( 4 x )}{65} + \frac{e x cos ( 4 x )}{65} - \frac{536 e}{4225} sin (4 x) + \frac{2 e}{4225} cos (4 x)

y = e^{x} (c_{1} cos (4 x) + c_{2} sin (4 x)) - \frac{8 e x sin ( 4 x )}{65} + \frac{e x cos ( 4 x )}{65} - \frac{536 e}{4225} sin (4 x) + \frac{2 e}{4225} cos (4 x)

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

y^{^{''}} - 8 y^{^{'}} + 20 y = 10 x e^{x}

7 y^{^{''}} + 7 y^{^{'}} + 2 y = 16 + 9 x + x^{2}

y^{^{''}} + y = - 8 x cos^{2} (x)

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 18 x^{2} - 4 x - 15