y^{'''}+144y^'=tan(12x)

Lösung

y^{^{'''}} + 144 y^{^{'}} = tan (12 x)

y = c_{1} + c_{2} cos (12 x) + c_{3} sin (12 x) + \frac{- ln ( cos ( 12 x ) ) + cos ^{2} ( 12 x ) - sin ( 12 x ) ( ln ( tan ( 12 x ) + sec ( 12 x ) ) - sin ( 12 x ) )}{1728}

Schritte zur Lösung

y^{'''} (x) + 144 y^{'} (x) = tan (12 x)

Solve linear ODE:

y = c_{1} + c_{2} cos (12 x) + c_{3} sin (12 x) + \frac{- ln ( cos ( 12 x ) ) + cos ^{2} ( 12 x ) - sin ( 12 x ) ( ln ( tan ( 12 x ) + sec ( 12 x ) ) - sin ( 12 x ) )}{1728}

y = c_{1} + c_{2} cos (12 x) + c_{3} sin (12 x) + \frac{- ln ( cos ( 12 x ) ) + cos ^{2} ( 12 x ) - sin ( 12 x ) ( ln ( tan ( 12 x ) + sec ( 12 x ) ) - sin ( 12 x ) )}{1728}

y^{^{''}} - 4 y^{^{'}} + 3 y = e^{4 x} (- 8 + 29 x + 12 x^{2})

y^{^{''}} + 4 y = 32 sin (2 x) + 16 cos (2 x)

5 y^{^{''}} + y^{^{'}} = - 6 x, y (0) = 0, y^{^{'}} (0) = - 10

y^{^{'''}} + y^{^{'}} = sin (x)

y^{^{''}} + 2 y^{^{'}} + y = \frac{ln ( x )}{e ^{x}}