(d^2y)/(dx^2)-5(dy)/(dx)+8y=xe^x

Lösung

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 8 y = x e^{x}

y = e^{\frac{5 x}{2}} (c_{1} cos (\frac{7 x}{2}) + c_{2} sin (\frac{7 x}{2})) + \frac{e ^{x} x}{4} + \frac{3}{16} e^{x}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 8 y = x e^{x}

Solve linear ODE:

y = e^{\frac{5 x}{2}} (c_{1} cos (\frac{7 x}{2}) + c_{2} sin (\frac{7 x}{2})) + \frac{e ^{x} x}{4} + \frac{3}{16} e^{x}

y = e^{\frac{5 x}{2}} (c_{1} cos (\frac{7 x}{2}) + c_{2} sin (\frac{7 x}{2})) + \frac{e ^{x} x}{4} + \frac{3}{16} e^{x}

y^{^{''}} - 9 y^{^{'}} + 14 y = 12 - e^{x}

y^{^{''}} + 2 y^{^{'}} + 5 y = 45, y (0) = 2, y^{^{'}} (0) = 3

y^{^{''}} + y^{^{'}} - 20 y = e^{x} (82 + 84 x - 36 x^{2})

x^{^{''}} + x - 6 = 0

y^{^{''}} + g^{2} y = cos (2 t), y (0) = 1, y^{^{'}} (0) = 0