y^{''}-8y^'+20y=200x^2-65xe^x

Lösung

y^{^{''}} - 8 y^{^{'}} + 20 y = 200 x^{2} - 65 x e^{x}

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 10 x^{2} + 8 x + \frac{11}{5} - 5 x e^{x} - \frac{30}{13} e^{x}

Schritte zur Lösung

y^{''} (x) - 8 y^{'} (x) + 20 y = 200 x^{2} - 65 x e^{x}

Solve linear ODE:

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 10 x^{2} + 8 x + \frac{11}{5} - 5 x e^{x} - \frac{30}{13} e^{x}

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 10 x^{2} + 8 x + \frac{11}{5} - 5 x e^{x} - \frac{30}{13} e^{x}

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{t}

y^{^{'''}} - y^{^{''}} - 8 y^{^{'}} + 12 y = 2 e^{t}

x^{^{''}} + 2 x^{^{'}} + x = e^{- t}

y^{^{''}} - 2 y^{^{'}} - 3 y = cos (2 t)

y^{^{''}} - 5 y^{^{'}} + 6 y = 5 e^{2 x}