y^{''}-8y^'+5y=xe^x

Lösung

y^{^{''}} - 8 y^{^{'}} + 5 y = x e^{x}

y = c_{1} e^{(4 + 11) x} + c_{2} e^{(4 - 11) x} - \frac{e ^{x} x}{2} + \frac{3}{2} e^{x}

Schritte zur Lösung

y^{''} (x) - 8 y^{'} (x) + 5 y = x e^{x}

Solve linear ODE:

y = c_{1} e^{(4 + 11) x} + c_{2} e^{(4 - 11) x} - \frac{e ^{x} x}{2} + \frac{3}{2} e^{x}

y = c_{1} e^{(4 + 11) x} + c_{2} e^{(4 - 11) x} - \frac{e ^{x} x}{2} + \frac{3}{2} e^{x}

\frac{d ^{2} y}{d t ^{2}} + 3 \frac{d y}{d t} + 5 y = sin (t)

y^{^{''}} - y = x e^{2 x}, y (0) = 0, y^{^{'}} (0) = 1

d (x) = \frac{9}{x}

y^{^{''}} + 4 y = t^{2} + 10 e^{t}, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} - y^{^{'}} + 12 y = t, y (0) = 1, y^{^{'}} (0) = 1