2x^{''}+3x^'+4x=-5cos(t)+sin(t)

Lösung

2 x^{^{''}} + 3 x^{^{'}} + 4 x = - 5 cos (t) + sin (t)

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

Schritte zur Lösung

2 x^{''} (t) + 3 x^{'} (t) + 4 x = - 5 cos (t) + sin (t)

Solve linear ODE:

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

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

y^{^{''}} + 2 y^{^{'}} + 2 y = e^{- x} \cdot cos (x)

y^{^{''}} + 6 y^{^{'}} + 5 y = 30

4 y^{^{''}} - 4 y^{^{'}} + y = 80 e^{\frac{t}{2}}

- 2 y^{^{''}} + y = e^{- 0.2 x}, y (0) = 1, y^{^{'}} (1) = - y (1)

y^{^{''}} - 64 y = sinh (8 x)