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Beliebt Rechnen >

y^{''}+9y^'=8sin(t),y(0)=1,y^'(0)=1

Lösung

y^{^{''}} + 9 y^{^{'}} = 8 sin (t), y (0) = 1, y^{^{'}} (0) = 1

Lösung

y = \frac{5}{41} + \frac{77}{41} - \frac{5}{41} e^{- 9 t} - \frac{4}{41} sin (t) - \frac{36}{41} cos (t)

Schritte zur Lösung

y^{''} (t) + 9 y^{'} (t) = 8 sin (t)

Solve linear ODE:

y = \frac{5}{41} + \frac{77}{41} - \frac{5}{41} e^{- 9 t} - \frac{4}{41} sin (t) - \frac{36}{41} cos (t)

y = \frac{5}{41} + \frac{77}{41} - \frac{5}{41} e^{- 9 t} - \frac{4}{41} sin (t) - \frac{36}{41} cos (t)

Graph

Beliebte Beispiele

y^{''}+2y^'+17=0,y(0)=1,y^'(0)=-1

y^{^{''}} + 2 y^{^{'}} + 17 = 0, y (0) = 1, y^{^{'}} (0) = - 1

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

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

y^{''}+40y^'+400y=100sin(10t)

y^{^{''}} + 40 y^{^{'}} + 400 y = 100 sin (10 t)

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

y^{''}-y^'-6y=14cos(3x)

y^{^{''}} - y^{^{'}} - 6 y = 14 cos (3 x)