y^{''}-5y^'+7y=3e^{5t}

Lösung

y^{^{''}} - 5 y^{^{'}} + 7 y = 3 e^{5 t}

y = e^{\frac{5 t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) + \frac{3}{7} e^{5 t}

Schritte zur Lösung

y^{''} (t) - 5 y^{'} (t) + 7 y = 3 e^{5 t}

Solve linear ODE:

y = e^{\frac{5 t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) + \frac{3}{7} e^{5 t}

y = e^{\frac{5 t}{2}} (c_{1} cos (\frac{3 t}{2}) + c_{2} sin (\frac{3 t}{2})) + \frac{3}{7} e^{5 t}

y^{^{''}} + y = sin (2 t), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 2 y^{^{'}} + 5 y = 2 e^{- x}, y (0) = 0, y^{^{'}} (0) = 2

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

- y^{^{'''}} - y^{^{'}} = 2 cos (t)

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 t + 6