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Beliebt Rechnen >

y^{''}+2y^'+10y=2cos(x)+cos(3x)

Lösung

y^{^{''}} + 2 y^{^{'}} + 10 y = 2 cos (x) + cos (3 x)

Lösung

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{4}{85} sin (x) + \frac{18}{85} cos (x) + \frac{6}{37} sin (3 x) + \frac{1}{37} cos (3 x)

Schritte zur Lösung

y^{''} (x) + 2 y^{'} (x) + 10 y = 2 cos (x) + cos (3 x)

Solve linear ODE:

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{4}{85} sin (x) + \frac{18}{85} cos (x) + \frac{6}{37} sin (3 x) + \frac{1}{37} cos (3 x)

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{4}{85} sin (x) + \frac{18}{85} cos (x) + \frac{6}{37} sin (3 x) + \frac{1}{37} cos (3 x)

Graph

Beliebte Beispiele

y^{''}+100y^'+2500y=20

y^{''}-y^'-2y=4

y^{''}-4y^'-y-2=0

x^{''}+4x=10cos(3t)

y^{''}+9y=12xe^{2x}