y^{''}+y=e^tsin(t),y(0)=0,y^'(0)=0

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

\frac{1}{2} y^{^{''}} + 5 y^{^{'}} + 12 y = e^{- 4 x} (4 x - 2)

2 y^{^{''}} + 5 y^{^{'}} + 2 y = x^{3} + 9 e^{4 x}

y^{^{''}} + y = sin (t), y (0) = 9, y^{^{'}} (0) = 1

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

3 x^{^{''}} + 108 x = 15 e^{- 5 t} cos (4 t)