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Beliebt Rechnen >

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

Lösung

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

Lösung

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{e ^{x} x}{7} - \frac{4}{49} e^{x}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{e ^{x} x}{7} - \frac{4}{49} e^{x}

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{e ^{x} x}{7} - \frac{4}{49} e^{x}

Graph

Beliebte Beispiele

y^{''}+25y=3,y(0)=1,y(0)=5

y^{^{''}} + 25 y = 3, y (0) = 1, y (0) = 5

y^{''}+6y^'+8y=2t-3cos(3t)

y^{^{''}} + 6 y^{^{'}} + 8 y = 2 t - 3 cos (3 t)

x^{''}+10x^'+25x=5sin(3t)

x^{^{''}} + 10 x^{^{'}} + 25 x = 5 sin (3 t)

y^{''}-4y=cos(2t)

y^{^{''}} - 4 y = cos (2 t)

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

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