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Beliebt Rechnen >

y^{''}+4y^'+13y=cos(3x)

Lösung

y^{^{''}} + 4 y^{^{'}} + 13 y = cos (3 x)

Lösung

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

Schritte zur Lösung

y^{''} (x) + 4 y^{'} (x) + 13 y = cos (3 x)

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

4y^{''}-y=sin(x)

4 y^{^{''}} - y = sin (x)

y^{''}+4y^'+4y=6x+7

y^{^{''}} + 4 y^{^{'}} + 4 y = 6 x + 7

y^{'''}+y^{''}+y^'+y=sin(3x)

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = sin (3 x)

y^{''}-5y^'+4y=cos(x)

y^{^{''}} - 5 y^{^{'}} + 4 y = cos (x)

y^{''}+9y=2e^{3t}+2cos(2t)

y^{^{''}} + 9 y = 2 e^{3 t} + 2 cos (2 t)