2y^{''}+18y=3tan(3x)

Lösung

2 y^{^{''}} + 18 y = 3 tan (3 x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{- 2 cos ( 3 x ) ( ln ( tan ( 3 x ) + sec ( 3 x ) ) - sin ( 3 x ) ) - sin ( 6 x )}{12}

Schritte zur Lösung

2 y^{''} (x) + 18 y = 3 tan (3 x)

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{- 2 cos ( 3 x ) ( ln ( tan ( 3 x ) + sec ( 3 x ) ) - sin ( 3 x ) ) - sin ( 6 x )}{12}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{- 2 cos ( 3 x ) ( ln ( tan ( 3 x ) + sec ( 3 x ) ) - sin ( 3 x ) ) - sin ( 6 x )}{12}

y^{^{''}} + y = e^{- 2 t} sin (t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} + 4 y^{^{'}} + 4 y = x^{3} e^{2 x}

y^{^{''}} - y^{^{'}} - 5 y = 5 t + 7

y^{^{''}} + 3 y = - 48 x e^{3 x}

y^{^{''}} + 8 y^{^{'}} + 8 y = cos (4 x)