y^{''}+4y=sin(x)*sin(2x)

Lösung

y^{^{''}} + 4 y = sin (x) \cdot sin (2 x)

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{1}{2} cos (2 x) (- \frac{1}{5} cos (5 x) - \frac{1}{3} cos (3 x) - sin^{2} (2 x) cos (x)) + \frac{1}{8} sin (2 x) (- \frac{1}{5} sin (5 x) + \frac{1}{3} sin (3 x))

Schritte zur Lösung

y^{''} (x) + 4 y = sin (x) \cdot sin (2 x)

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{1}{2} cos (2 x) (- \frac{1}{5} cos (5 x) - \frac{1}{3} cos (3 x) - sin^{2} (2 x) cos (x)) + \frac{1}{8} sin (2 x) (- \frac{1}{5} sin (5 x) + \frac{1}{3} sin (3 x))

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{1}{2} cos (2 x) (- \frac{1}{5} cos (5 x) - \frac{1}{3} cos (3 x) - sin^{2} (2 x) cos (x)) + \frac{1}{8} sin (2 x) (- \frac{1}{5} sin (5 x) + \frac{1}{3} sin (3 x))

y^{^{''}} + y^{^{'}} = cos (x), y (0) = 0, y^{^{'}} (0) = 1

4 y^{^{''}} - y = e^{(\frac{x}{2})} + 5

x^{^{''}} + 64 x = sin (5 t)

0.5 y^{^{''}} + 50 y = cos (t)

x^{^{''}} + x = 1, x (0) = 2, x^{^{'}} (0) = - 1