y^{''}+4y=11sec^2(2t)

Lösung

y^{^{''}} + 4 y = 11 sec^{2} (2 t)

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 11 cos ( 2 t ) ( cos ( 2 t ) + sin ( 2 t ) tan ( 2 t ) ) + 11 ln ( tan ( 2 t ) + sec ( 2 t ) ) sin ( 2 t )}{4}

Schritte zur Lösung

y^{''} (t) + 4 y = 11 sec^{2} (2 t)

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 11 cos ( 2 t ) ( cos ( 2 t ) + sin ( 2 t ) tan ( 2 t ) ) + 11 ln ( tan ( 2 t ) + sec ( 2 t ) ) sin ( 2 t )}{4}

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{- 11 cos ( 2 t ) ( cos ( 2 t ) + sin ( 2 t ) tan ( 2 t ) ) + 11 ln ( tan ( 2 t ) + sec ( 2 t ) ) sin ( 2 t )}{4}

y^{^{''}} - 5 y^{^{'}} + 4 y = 2 e^{x} + x + 1

4 y^{^{''}} - 8 y^{^{'}} + 3 = 0, y (0) = 2, y^{^{'}} (0) = \frac{1}{2}

y^{^{'''}} - 9 y^{^{''}} + 27 y = 3 e^{3 x}

y^{^{''}} + 7 y^{^{'}} = x + e^{2 x}

(D^{2} - 1) y = x^{2} e^{\frac{x ^{2}}{2}}