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Beliebt Rechnen >

y^{''}-4y^'+8y=12xe^{2x}+6e^{2x}

Lösung

y^{^{''}} - 4 y^{^{'}} + 8 y = 12 x e^{2 x} + 6 e^{2 x}

Lösung

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

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) + 8 y = 12 x e^{2 x} + 6 e^{2 x}

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+y=8xcos(x)

y^{^{''}} + y = 8 x cos (x)

(D^2-6D+9)y=x^2e^{2x}

(D^{2} - 6 D + 9) y = x^{2} e^{2 x}

y^{''}+2y^'+10=0,y(0)=-2,y^'(0)=0

y^{^{''}} + 2 y^{^{'}} + 10 = 0, y (0) = - 2, y^{^{'}} (0) = 0

4y^{''}+y=10cos(x)

4 y^{^{''}} + y = 10 cos (x)

y^{''}+4y^'+4y=8e^{-2}x

y^{^{''}} + 4 y^{^{'}} + 4 y = 8 e^{- 2} x