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

Lösung

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

y = e^{\frac{3 t}{2}} (c_{1} cos (\frac{19 t}{2}) + c_{2} sin (\frac{19 t}{2})) + \frac{3}{7} e^{3 t}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{\frac{3 t}{2}} (c_{1} cos (\frac{19 t}{2}) + c_{2} sin (\frac{19 t}{2})) + \frac{3}{7} e^{3 t}

y = e^{\frac{3 t}{2}} (c_{1} cos (\frac{19 t}{2}) + c_{2} sin (\frac{19 t}{2})) + \frac{3}{7} e^{3 t}

y^{^{''}} + 6 y^{^{'}} = - 9

y^{^{''}} + 4 y^{^{'}} + 8 y = 24, y^{^{'}} (0) = 0, y (0) = 0

y^{^{''}} + 18 y^{^{'}} - y = t^{- 1} e^{t}

D B = 10 lo g_{10} (\frac{0.1}{1 \cdot 1 0 ^{- 12}})

y^{^{''}} - 8 y^{^{'}} + 16 y = 32 t + 64, y (0) = 3, y^{^{'}} (0) = - 3