y^{''}+16y=11sec^2(4t)

Lösung

y^{^{''}} + 16 y = 11 sec^{2} (4 t)

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 11 + 11 ln ( tan ( 4 t ) + sec ( 4 t ) ) sin ( 4 t )}{16}

Schritte zur Lösung

y^{''} (t) + 16 y = 11 sec^{2} (4 t)

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 11 + 11 ln ( tan ( 4 t ) + sec ( 4 t ) ) sin ( 4 t )}{16}

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{- 11 + 11 ln ( tan ( 4 t ) + sec ( 4 t ) ) sin ( 4 t )}{16}

y^{^{''}} - 4 y^{^{'}} - 12 y = 2 sin (t)

12 y^{^{''}} + 29 y^{^{'}} - 11 y = - 9

y^{^{''}} - 9 y = 2

y^{^{''}} - y = - 10 t + 4

y^{^{''}} - 10 y^{^{'}} + 25 y = e^{5} x ln (4 + x^{2})