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Beliebt Rechnen >

y^{''}+3y^'+21y=9cos(4t)

Lösung

y^{^{''}} + 3 y^{^{'}} + 21 y = 9 cos (4 t)

Lösung

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{5 3 t}{2}) + c_{2} sin (\frac{5 3 t}{2})) + \frac{108}{169} sin (4 t) + \frac{45}{169} cos (4 t)

Schritte zur Lösung

y^{''} (t) + 3 y^{'} (t) + 21 y = 9 cos (4 t)

Solve linear ODE:

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{5 3 t}{2}) + c_{2} sin (\frac{5 3 t}{2})) + \frac{108}{169} sin (4 t) + \frac{45}{169} cos (4 t)

y = e^{- \frac{3 t}{2}} (c_{1} cos (\frac{5 3 t}{2}) + c_{2} sin (\frac{5 3 t}{2})) + \frac{108}{169} sin (4 t) + \frac{45}{169} cos (4 t)

Graph

Beliebte Beispiele

4y^{''}+7y^'-y=15

4 y^{^{''}} + 7 y^{^{'}} - y = 15

y^{''}+7y^'+12y=5e^{-6x}

y^{^{''}} + 7 y^{^{'}} + 12 y = 5 e^{- 6 x}

y^{''}-4y^'-45y=(7+2x)

y^{^{''}} - 4 y^{^{'}} - 45 y = (7 + 2 x)

y^{''}+81y=2sin(2x),y(0)=1,y^'(0)=0

y^{^{''}} + 81 y = 2 sin (2 x), y (0) = 1, y^{^{'}} (0) = 0

linear y^{''}-y=x,y(0)=0,y(1)=0

l in e a r y^{^{''}} - y = x, y (0) = 0, y (1) = 0