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Beliebt Rechnen >

y^{'''}+2y^'-y^'-2y=sin(3t)

Lösung

y^{^{'''}} + 2 y^{^{'}} - y^{^{'}} - 2 y = sin (3 t)

Lösung

y = c_{1} e^{t} + e^{- \frac{t}{2}} (c_{2} cos (\frac{7 t}{2}) + c_{3} sin (\frac{7 t}{2})) - \frac{1}{290} sin (3 t) + \frac{6}{145} cos (3 t)

Schritte zur Lösung

y^{'''} (t) + 2 y^{'} (t) - y^{'} (t) - 2 y = sin (3 t)

Solve linear ODE:

y = c_{1} e^{t} + e^{- \frac{t}{2}} (c_{2} cos (\frac{7 t}{2}) + c_{3} sin (\frac{7 t}{2})) - \frac{1}{290} sin (3 t) + \frac{6}{145} cos (3 t)

y = c_{1} e^{t} + e^{- \frac{t}{2}} (c_{2} cos (\frac{7 t}{2}) + c_{3} sin (\frac{7 t}{2})) - \frac{1}{290} sin (3 t) + \frac{6}{145} cos (3 t)

Graph

Beliebte Beispiele

(D^2+1)y=sec^2(x)

(D^{2} + 1) y = sec^{2} (x)

y^{''}+2y^'+y=e^{-t}sqrt(1+t)

y^{^{''}} + 2 y^{^{'}} + y = e^{- t} 1 + t

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

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

2y^{''}-y^'-3y=3xe^{2x}

2 y^{^{''}} - y^{^{'}} - 3 y = 3 x e^{2 x}

y^{''}+y=x^2+1,y(0)=3,y(1)=0

y^{^{''}} + y = x^{2} + 1, y (0) = 3, y (1) = 0