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Beliebt Rechnen >

y^{''}+2y^'+4y=-10xe^x

Lösung

y^{^{''}} + 2 y^{^{'}} + 4 y = - 10 x e^{x}

Lösung

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) - \frac{10 e ^{x} x}{7} + \frac{40}{49} e^{x}

Schritte zur Lösung

y^{''} (x) + 2 y^{'} (x) + 4 y = - 10 x e^{x}

Solve linear ODE:

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) - \frac{10 e ^{x} x}{7} + \frac{40}{49} e^{x}

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) - \frac{10 e ^{x} x}{7} + \frac{40}{49} e^{x}

Graph

Beliebte Beispiele

y^{''}+4y^'+5=50x+13e^{3x}

y^{^{''}} + 4 y^{^{'}} + 5 = 50 x + 13 e^{3 x}

(d^2y)/(dx^2)-6(dy)/(dx)=12x

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} = 12 x

y^{^{''}} + 3 y^{^{'}} = 3 x

y^{''}-y^'-2y=-4x^2-6x+1

y^{^{''}} - y^{^{'}} - 2 y = - 4 x^{2} - 6 x + 1

y^{''}-4y^'+5y=10x-3

y^{^{''}} - 4 y^{^{'}} + 5 y = 10 x - 3