2y^{''}+12y=6tan(3x)

Lösung

2 y^{^{''}} + 12 y = 6 tan (3 x)

y = c_{1} cos (6 x) + c_{2} sin (6 x) + cos (6 x) \cdot \int - \frac{6 sin ( 6 x ) tan ( 3 x )}{2} d x + sin (6 x) \cdot \int \frac{6 cos ( 6 x ) tan ( 3 x )}{2} d x

Schritte zur Lösung

2 y^{''} (x) + 12 y = 6 tan (3 x)

Solve linear ODE:

y = c_{1} cos (6 x) + c_{2} sin (6 x) + cos (6 x) \cdot \int - \frac{6 sin ( 6 x ) tan ( 3 x )}{2} d x + sin (6 x) \cdot \int \frac{6 cos ( 6 x ) tan ( 3 x )}{2} d x

y = c_{1} cos (6 x) + c_{2} sin (6 x) + cos (6 x) \cdot \int - \frac{6 sin ( 6 x ) tan ( 3 x )}{2} d x + sin (6 x) \cdot \int \frac{6 cos ( 6 x ) tan ( 3 x )}{2} d x

y^{^{''}} + 4 y^{^{'}} + 5 y = - 5 x + 3 e^{(- x)}

y^{^{''}} - 3 y^{^{'}} + 2 y = 11 e^{3} x, y^{1} (0) = e x

y^{^{''}} + 4 y = 8 x^{2} + 7 x

y^{^{''}} - 4 y^{^{'}} = x

y^{^{''}} + 3 y = cos (3 x)