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Beliebt Rechnen >

5y^{''}+6y^'+80y=-24sin(4t)

Lösung

5 y^{^{''}} + 6 y^{^{'}} + 80 y = - 24 sin (4 t)

Lösung

y = e^{- \frac{3 t}{5}} (c_{1} cos (\frac{391 t}{5}) + c_{2} sin (\frac{391 t}{5})) + cos (4 t)

Schritte zur Lösung

5 y^{''} (t) + 6 y^{'} (t) + 80 y = - 24 sin (4 t)

Solve linear ODE:

y = e^{- \frac{3 t}{5}} (c_{1} cos (\frac{391 t}{5}) + c_{2} sin (\frac{391 t}{5})) + cos (4 t)

y = e^{- \frac{3 t}{5}} (c_{1} cos (\frac{391 t}{5}) + c_{2} sin (\frac{391 t}{5})) + cos (4 t)

Graph

Beliebte Beispiele

y^{''}-y^'-2y=e^{-x}

y^{^{''}} - y^{^{'}} - 2 y = e^{- x}

y^{''}-3y^'-4y=x

y^{^{''}} - 3 y^{^{'}} - 4 y = x

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

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

(d^2y)/(dx^2)-5(dy)/(dx)+6y=3x

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = 3 x

y^{''}-y^'-12y=2t^6e^{-3t}

y^{^{''}} - y^{^{'}} - 12 y = 2 t^{6} e^{- 3 t}