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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{(4 + 14) x} + c_{2} e^{(4 - 14) x} - \frac{e ^{x} x}{5} + \frac{6}{25} e^{x}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{(4 + 14) x} + c_{2} e^{(4 - 14) x} - \frac{e ^{x} x}{5} + \frac{6}{25} e^{x}

y = c_{1} e^{(4 + 14) x} + c_{2} e^{(4 - 14) x} - \frac{e ^{x} x}{5} + \frac{6}{25} e^{x}

Graph

Beliebte Beispiele

y^{'''}-16y^'=t(e^{4t})

y^{^{'''}} - 16 y^{^{'}} = t (e^{4 t})

y^{''}-2y^'+y=0+e^{2x}

y^{^{''}} - 2 y^{^{'}} + y = 0 + e^{2 x}

y^{''}+2y=2,5e^{-t}y(0)=3

y^{^{''}} + 2 y = 2, 5 e^{- t} y (0) = 3

y^{''}+4y=5te^t

y^{^{''}} + 4 y = 5 t e^{t}

y^{''}-2y^'-12y=2x+6

y^{^{''}} - 2 y^{^{'}} - 12 y = 2 x + 6