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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} cos (t) + c_{2} sin (t) + \frac{1}{8} e^{- 2 t} sin (t) + \frac{1}{8} e^{- 2 t} cos (t) + \frac{t ^{2} sin ( t ) + t cos ( t )}{4}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t) + \frac{1}{8} e^{- 2 t} sin (t) + \frac{1}{8} e^{- 2 t} cos (t) + \frac{t ^{2} sin ( t ) + t cos ( t )}{4}

y = c_{1} cos (t) + c_{2} sin (t) + \frac{1}{8} e^{- 2 t} sin (t) + \frac{1}{8} e^{- 2 t} cos (t) + \frac{t ^{2} sin ( t ) + t cos ( t )}{4}

Graph

Beliebte Beispiele

y^{''}-4y^'=8e^6x(x-1)

y^{^{''}} - 4 y^{^{'}} = 8 e^{6} x (x - 1)

y^{''}+64y=sin(8x)

y^{^{''}} + 64 y = sin (8 x)

y^{''}+6y=t^4,y(0)=0,y^'(0)=0

y^{^{''}} + 6 y = t^{4}, y (0) = 0, y^{^{'}} (0) = 0

(D^2+2D-8)y=(6x^{-1}-x^{-2})e^{2x}

(D^{2} + 2 D - 8) y = (6 x^{- 1} - x^{- 2}) e^{2 x}

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

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