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Beliebt Rechnen >

(d^2-1)y=x^2e^x

Lösung

(d^{2} - 1) y = x^{2} e^{x}

Lösung

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{x} x ^{3}}{6} - \frac{e ^{x} x ^{2}}{4} + \frac{e ^{x} x}{4}

Schritte zur Lösung

(d^{2} - 1) y = x^{2} e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{x} x ^{3}}{6} - \frac{e ^{x} x ^{2}}{4} + \frac{e ^{x} x}{4}

y = c_{1} e^{x} + c_{2} e^{- x} + \frac{e ^{x} x ^{3}}{6} - \frac{e ^{x} x ^{2}}{4} + \frac{e ^{x} x}{4}

Graph

Beliebte Beispiele

x^{''}+4x^'-5x=4t^2

x^{^{''}} + 4 x^{^{'}} - 5 x = 4 t^{2}

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

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

y^{''}-4y=xe^{-x}

y^{^{''}} - 4 y = x e^{- x}

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

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

y^{''}+y^'-2y=(e^x+e^{-x})/2

y^{^{''}} + y^{^{'}} - 2 y = \frac{e ^{x} + e ^{- x}}{2}