y^{''}+2y^'+10y=17sin(x)-37sin(3x)

Lösung

y^{^{''}} + 2 y^{^{'}} + 10 y = 17 sin (x) - 37 sin (3 x)

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{9}{5} sin (x) - \frac{2}{5} cos (x) - sin (3 x) + 6 cos (3 x)

Schritte zur Lösung

y^{''} (x) + 2 y^{'} (x) + 10 y = 17 sin (x) - 37 sin (3 x)

Solve linear ODE:

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{9}{5} sin (x) - \frac{2}{5} cos (x) - sin (3 x) + 6 cos (3 x)

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{9}{5} sin (x) - \frac{2}{5} cos (x) - sin (3 x) + 6 cos (3 x)

y^{^{''}} + 5 y + 6 y = 10 sin (x), y (0) = 1, y^{^{'}} (0) = - 4

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 e^{e t}, y (0) = - 3, y^{^{'}} (0) = 5

y^{^{''}} + 8 y = 2 t^{4}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = x^{- 1} e^{2 x}

16 y^{^{''}} - 24 y^{^{'}} + 9 y = 5 - 3 x