y^{''''}+9y^{''}=sec^2(3t)

Lösung

y^{^{''''}} + 9 y^{^{''}} = sec^{2} (3 t)

y = c_{1} + c_{2} t + c_{3} cos (3 t) + c_{4} sin (3 t) + \frac{- 9 t ^{2} sec ^{2} ( 3 t ) + 9 t ^{2} tan ^{2} ( 3 t ) + 9 t ^{2} - 2 ln ( cos ( 3 t ) ) - 2 ln ( tan ( 3 t ) + sec ( 3 t ) ) sin ( 3 t ) + 2}{162}

Schritte zur Lösung

y^{(4)} (t) + 9 y^{''} (t) = sec^{2} (3 t)

Solve linear ODE:

y = c_{1} + c_{2} t + c_{3} cos (3 t) + c_{4} sin (3 t) + \frac{- 9 t ^{2} sec ^{2} ( 3 t ) + 9 t ^{2} tan ^{2} ( 3 t ) + 9 t ^{2} - 2 ln ( cos ( 3 t ) ) - 2 ln ( tan ( 3 t ) + sec ( 3 t ) ) sin ( 3 t ) + 2}{162}

y = c_{1} + c_{2} t + c_{3} cos (3 t) + c_{4} sin (3 t) + \frac{- 9 t ^{2} sec ^{2} ( 3 t ) + 9 t ^{2} tan ^{2} ( 3 t ) + 9 t ^{2} - 2 ln ( cos ( 3 t ) ) - 2 ln ( tan ( 3 t ) + sec ( 3 t ) ) sin ( 3 t ) + 2}{162}

y^{^{''}} - 8 y^{^{'}} + 16 y = 8 x + 7

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

y^{^{''}} - 16 y = (x + 1) e^{x}

y^{^{''}} + 9 y = 13 e^{2 x} + 10 sin (2 x)

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