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

Lösung

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

y = c_{1} cos (\frac{t}{3}) + c_{2} sin (\frac{t}{3}) - \frac{1}{2} cos (t)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} cos (\frac{t}{3}) + c_{2} sin (\frac{t}{3}) - \frac{1}{2} cos (t)

y = c_{1} cos (\frac{t}{3}) + c_{2} sin (\frac{t}{3}) - \frac{1}{2} cos (t)

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

- y^{^{''}} + y^{^{'}} = 1

y^{^{''}} - 4 y^{^{'}} + 3 y = 4 e^{3 t}, y (0) = 2, y^{^{'}} (0) = 7

\frac{1}{8} y^{^{''}} + 4 y^{^{'}} + 28 x = 0, y (0) = 0, y^{^{'}} (0) = 3

- 6 y^{^{''}} - 5 y^{^{'}} - y = - (t^{2} + 2 t + 2 e^{2 t})