y^{''}+4y=8tan(t)

Lösung

y^{^{''}} + 4 y = 8 tan (t)

y = c_{1} cos (2 t) + c_{2} sin (2 t) - 4 cos (2 t) (t - \frac{1}{2} sin (2 t)) + 2 sin (2 t) (tan (t) sin (2 t) + ln (cos^{2} (t)))

Schritte zur Lösung

y^{''} (t) + 4 y = 8 tan (t)

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) - 4 cos (2 t) (t - \frac{1}{2} sin (2 t)) + 2 sin (2 t) (tan (t) sin (2 t) + ln (cos^{2} (t)))

y = c_{1} cos (2 t) + c_{2} sin (2 t) - 4 cos (2 t) (t - \frac{1}{2} sin (2 t)) + 2 sin (2 t) (tan (t) sin (2 t) + ln (cos^{2} (t)))

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

y^{^{''}} - 9 y = 1, y (0) = 0

y^{^{''}} - 4 y^{^{'}} + 4 y = - 7 x + 4 x^{2}, y (0) = 0, y^{^{'}} (0) = 1

3 y^{^{''}} + 3 y^{^{'}} - 6 y = 4 e^{- 2 x}

y^{^{''}} + y = cos (\frac{- t + π}{2})