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Beliebt Rechnen >

y^{''}+2y^'+5y=e^xsin(x)

Lösung

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

Lösung

y = e^{- x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{7}{65} e^{x} sin (x) - \frac{4}{65} e^{x} cos (x)

Schritte zur Lösung

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

Solve linear ODE:

y = e^{- x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{7}{65} e^{x} sin (x) - \frac{4}{65} e^{x} cos (x)

y = e^{- x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + \frac{7}{65} e^{x} sin (x) - \frac{4}{65} e^{x} cos (x)

Graph

Beliebte Beispiele

y^{''}+y= 1/(sin^2(x))

y^{^{''}} + y = \frac{1}{sin ^{2} ( x )}

5y^{''}+10y^'=3x^2

5 y^{^{''}} + 10 y^{^{'}} = 3 x^{2}

x^{''}+4x^'+3x=sin(e^t)

x^{^{''}} + 4 x^{^{'}} + 3 x = sin (e^{t})

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

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

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

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} = x