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Beliebt Rechnen >

(d^2y)/(dx^2)-(dy)/(dx)+1/4 y=xe^{x/2}

Lösung

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} + \frac{1}{4} y = x e^{\frac{x}{2}}

Lösung

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + \frac{e ^{\frac{x}{2}} x ^{3}}{6}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} + \frac{1}{4} y = x e^{\frac{x}{2}}

Solve linear ODE:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + \frac{e ^{\frac{x}{2}} x ^{3}}{6}

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{\frac{x}{2}} x + \frac{e ^{\frac{x}{2}} x ^{3}}{6}

Graph

Beliebte Beispiele

x^{''}+4x=sin(t)

x^{^{''}} + 4 x = sin (t)

3y^{''}-2y^'-y=x^2

3 y^{^{''}} - 2 y^{^{'}} - y = x^{2}

D (t) = t + 5

y^{''}+2y^'-y=t^{-1}e^t

y^{^{''}} + 2 y^{^{'}} - y = t^{- 1} e^{t}

y^{''}-2y^'+2y=sin(t),y(0)=0,y^'(0)=1

y^{^{''}} - 2 y^{^{'}} + 2 y = sin (t), y (0) = 0, y^{^{'}} (0) = 1