2y^{''}+y^'+3y=33cos(3t)-22sin(3t)

Lösung

2 y^{^{''}} + y^{^{'}} + 3 y = 33 cos (3 t) - 22 sin (3 t)

y = e^{- \frac{t}{4}} (c_{1} cos (\frac{23 t}{4}) + c_{2} sin (\frac{23 t}{4})) + \frac{11}{6} sin (3 t) - \frac{11}{6} cos (3 t)

Schritte zur Lösung

2 y^{''} (t) + y^{'} (t) + 3 y = 33 cos (3 t) - 22 sin (3 t)

Solve linear ODE:

y = e^{- \frac{t}{4}} (c_{1} cos (\frac{23 t}{4}) + c_{2} sin (\frac{23 t}{4})) + \frac{11}{6} sin (3 t) - \frac{11}{6} cos (3 t)

y = e^{- \frac{t}{4}} (c_{1} cos (\frac{23 t}{4}) + c_{2} sin (\frac{23 t}{4})) + \frac{11}{6} sin (3 t) - \frac{11}{6} cos (3 t)

d (x) = \frac{x ^{2} - 12 x + 20}{3 x}

4 y^{^{''}} + 16 y = 17 sec^{2} (4 t)

- y^{^{''}} + y = e^{1 \cdot x}, y (0) = 0, y (1) = 0

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

y^{^{''}} - 9 y = 24