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Beliebt Rechnen >

y^{''}-3y^'+5y=xe^x

Lösung

y^{^{''}} - 3 y^{^{'}} + 5 y = x e^{x}

Lösung

y = e^{\frac{3 x}{2}} (c_{1} cos (\frac{11 x}{2}) + c_{2} sin (\frac{11 x}{2})) + \frac{e ^{x} x}{3} + \frac{1}{9} e^{x}

Schritte zur Lösung

y^{''} (x) - 3 y^{'} (x) + 5 y = x e^{x}

Solve linear ODE:

y = e^{\frac{3 x}{2}} (c_{1} cos (\frac{11 x}{2}) + c_{2} sin (\frac{11 x}{2})) + \frac{e ^{x} x}{3} + \frac{1}{9} e^{x}

y = e^{\frac{3 x}{2}} (c_{1} cos (\frac{11 x}{2}) + c_{2} sin (\frac{11 x}{2})) + \frac{e ^{x} x}{3} + \frac{1}{9} e^{x}

Graph

Beliebte Beispiele

(dx)/(dt)+2t^3x^5+x/t =0

\frac{d x}{d t} + 2 t^{3} x^{5} + \frac{x}{t} = 0

derivative of 5x^2+sin(xcos(x))

\frac{d}{d x} (5 x^{2} + sin (x) cos (x))

y^{^{'}} = y (x y^{5} + 2)

f (t) = t cos (t)

(\partial)/(\partial y)(sin(x))

\frac{\partial}{\partial y} (sin (x))