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Beliebt Rechnen >

y^{''}+y^'-2y=e^tsin(t),y(0)=0,y^'(0)=0

Lösung

y^{^{''}} + y^{^{'}} - 2 y = e^{t} sin (t), y (0) = 0, y^{^{'}} (0) = 0

Lösung

y = (\frac{1}{30} + \frac{3}{10}) e^{t} - \frac{1}{30} e^{- 2 t} - \frac{1}{10} e^{t} sin (t) - \frac{3}{10} e^{t} cos (t)

Schritte zur Lösung

y^{''} (t) + y^{'} (t) - 2 y = e^{t} sin (t)

Solve linear ODE:

y = (\frac{1}{30} + \frac{3}{10}) e^{t} - \frac{1}{30} e^{- 2 t} - \frac{1}{10} e^{t} sin (t) - \frac{3}{10} e^{t} cos (t)

y = (\frac{1}{30} + \frac{3}{10}) e^{t} - \frac{1}{30} e^{- 2 t} - \frac{1}{10} e^{t} sin (t) - \frac{3}{10} e^{t} cos (t)

Graph

Beliebte Beispiele

y^{''}+22y^'+121y=16.3u

y^{^{''}} + 22 y^{^{'}} + 121 y = 16.3 u

y^{''}+y=2e^{-8t},y(0)=0,y^'(0)=0

y^{^{''}} + y = 2 e^{- 8 t}, y (0) = 0, y^{^{'}} (0) = 0

y^{'''}-6y^'-7=0

y^{^{'''}} - 6 y^{^{'}} - 7 = 0

(d^2y)/(dx^2)+9y=15x^2-9

\frac{d ^{2} y}{d x ^{2}} + 9 y = 15 x^{2} - 9

y^{''}+6y^'+8y=2t+e^t,y(0)=0,y^'(0)=0

y^{^{''}} + 6 y^{^{'}} + 8 y = 2 t + e^{t}, y (0) = 0, y^{^{'}} (0) = 0