y^{''}+4y^'+5y=25x^2+13sin(2x)

Lösung

y^{^{''}} + 4 y^{^{'}} + 5 y = 25 x^{2} + 13 sin (2 x)

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + 5 x^{2} - 8 x + \frac{22}{5} + \frac{1}{5} sin (2 x) - \frac{8}{5} cos (2 x)

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 5 y = 25 x^{2} + 13 sin (2 x)

Solve linear ODE:

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + 5 x^{2} - 8 x + \frac{22}{5} + \frac{1}{5} sin (2 x) - \frac{8}{5} cos (2 x)

y = e^{- 2 x} (c_{1} cos (x) + c_{2} sin (x)) + 5 x^{2} - 8 x + \frac{22}{5} + \frac{1}{5} sin (2 x) - \frac{8}{5} cos (2 x)

y^{^{''}} + 2 y^{^{'}} - 3 y = 4 e^{- 3 x} + 10 sin (x)

y^{^{''''}} + 2 y^{^{''}} + y = 9 t + 10

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

y^{^{''}} - 6 y^{^{'}} + 9 y = x + 1

7 y^{^{''}} = 5 y - \frac{3}{2} x^{2}, y (0) = 0, y^{^{'}} (2) = 0