y^{''}+(-8)y^'+20y=100x^2-65xe^x

Lösung

y^{^{''}} + (- 8) y^{^{'}} + 20 y = 100 x^{2} - 65 x e^{x}

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} + 4 x + \frac{11}{10} - 5 x e^{x} - \frac{30}{13} e^{x}

Schritte zur Lösung

y^{''} (x) + (- 8) y^{'} (x) + 20 y = 100 x^{2} - 65 x e^{x}

Solve linear ODE:

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} + 4 x + \frac{11}{10} - 5 x e^{x} - \frac{30}{13} e^{x}

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} + 4 x + \frac{11}{10} - 5 x e^{x} - \frac{30}{13} e^{x}

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

(D^{2} + D - 12) y = x

y^{^{''}} - 8 y^{^{'}} + 16 y = (x - 1) e^{4 x}

y^{^{''}} - 5 y^{^{'}} - 14 y = e^{x} (x + 1)

l in e a r y^{^{''}} + 4 y = e^{3 t}, y (0) = 0, y^{^{'}} (0) = 0