y^{''}-8y^'+20y=100x^2-39xe^x

Lösung

y^{^{''}} - 8 y^{^{'}} + 20 y = 100 x^{2} - 39 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} - 3 x e^{x} - \frac{18}{13} e^{x}

Schritte zur Lösung

y^{''} (x) - 8 y^{'} (x) + 20 y = 100 x^{2} - 39 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} - 3 x e^{x} - \frac{18}{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} - 3 x e^{x} - \frac{18}{13} e^{x}

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

y^{^{''}} + y = sin (3 x)

y^{^{'''}} - 6 y^{^{''}} + 12 y^{^{'}} - 8 y = 16 e^{- 2 t}

y^{^{''}} - 2 y^{^{'}} = cos (4 x)

4 y^{^{''}} - y = 12 + 6 x