linear y^{''}+y^'+2y=sin(x)

Lösung

linear

y^{^{''}} + y^{^{'}} + 2 y = sin (x)

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

Schritte zur Lösung

y^{''} (x) + y^{'} (x) + 2 y = sin (x)

Solve linear ODE:

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

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

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

y^{^{''}} - 15 y^{^{'}} + 54 y = e^{a x}

y^{^{'''}} + 9 y^{^{''}} + y^{^{'}} + 9 y = 16 e^{x} - 9

y^{^{''}} + 8 y^{^{'}} + 32 y = 2 e^{2 x}

y^{^{''}} + y - 2 = 5 e^{- 2 x}