(d^2y)/(dx^2)-4(dy)/(dx)+5y=xe^x

Lösung

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 5 y = x e^{x}

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

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 5 y = x e^{x}

Solve linear ODE:

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

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

x^{^{''}} + 200 x^{^{'}} + 100000 x = 100 sin (100 t)

2 y^{^{''}} + 6 y^{^{'}} + 10 y = 4 cos (t)

y^{^{''}} - 14 y^{^{'}} + 49 y = 2 x e^{7 x}

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3} x, y (0) = - 1, y^{^{'}} (0) = 1

\frac{d ^{2} y}{d t ^{2}} - 5 \frac{d y}{d t} + 6 = 0