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Beliebt Rechnen >

y^{''}+3y^'+5y=sin(t),y(0)=1,y^'(0)=0

Lösung

y^{^{''}} + 3 y^{^{'}} + 5 y = sin (t), y (0) = 1, y^{^{'}} (0) = 0

Lösung

y = e^{- \frac{3 t}{2}} (\frac{28}{25} cos (\frac{11 t}{2}) + \frac{76}{25 11} sin (\frac{11 t}{2})) + \frac{4}{25} sin (t) - \frac{3}{25} cos (t)

Schritte zur Lösung

y^{''} (t) + 3 y^{'} (t) + 5 y = sin (t)

Solve linear ODE:

y = e^{- \frac{3 t}{2}} (\frac{28}{25} cos (\frac{11 t}{2}) + \frac{76}{25 11} sin (\frac{11 t}{2})) + \frac{4}{25} sin (t) - \frac{3}{25} cos (t)

y = e^{- \frac{3 t}{2}} (\frac{28}{25} cos (\frac{11 t}{2}) + \frac{76}{25 11} sin (\frac{11 t}{2})) + \frac{4}{25} sin (t) - \frac{3}{25} cos (t)

Graph

Beliebte Beispiele

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

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

y^{''}-4y=6x-4x^3

y^{^{''}} - 4 y = 6 x - 4 x^{3}

y^{'''}-y^{''}+4y^'-4y=-3e^t+4e^{2t}

y^{^{'''}} - y^{^{''}} + 4 y^{^{'}} - 4 y = - 3 e^{t} + 4 e^{2 t}

y^{''}-8y^'+16y=8+16x

y^{^{''}} - 8 y^{^{'}} + 16 y = 8 + 16 x

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

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