y^{'''}+256y^'=tan(16x)

Lösung

y^{^{'''}} + 256 y^{^{'}} = tan (16 x)

y = c_{1} + c_{2} cos (16 x) + c_{3} sin (16 x) + \frac{- ln ( cos ( 16 x ) ) + cos ^{2} ( 16 x ) - sin ( 16 x ) ( ln ( tan ( 16 x ) + sec ( 16 x ) ) - sin ( 16 x ) )}{4096}

Schritte zur Lösung

y^{'''} (x) + 256 y^{'} (x) = tan (16 x)

Solve linear ODE:

y = c_{1} + c_{2} cos (16 x) + c_{3} sin (16 x) + \frac{- ln ( cos ( 16 x ) ) + cos ^{2} ( 16 x ) - sin ( 16 x ) ( ln ( tan ( 16 x ) + sec ( 16 x ) ) - sin ( 16 x ) )}{4096}

y = c_{1} + c_{2} cos (16 x) + c_{3} sin (16 x) + \frac{- ln ( cos ( 16 x ) ) + cos ^{2} ( 16 x ) - sin ( 16 x ) ( ln ( tan ( 16 x ) + sec ( 16 x ) ) - sin ( 16 x ) )}{4096}

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

y^{^{''}} + 6 y^{^{'}} + 5 y = 15

y^{^{''}} + 3 y^{^{'}} + 2 y = 1 + 3 x + x^{2}

y^{^{''}} - y = e^{2 t} t^{2}

y^{^{''}} + y^{^{'}} - 2 y = 6