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

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

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

y^{^{''}} + 6 y^{^{'}} + 9 y = 50 e^{2 x}

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 5 y = x \cdot e^{2 x}

2 y^{^{''}} + 3 y^{^{'}} + y = e^{- 3 x}

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