(d^2y)/(dx^2)+c^2y=sec^2(cx)

Lösung

\frac{d ^{2} y}{d x ^{2}} + c^{2} y = sec^{2} (c x)

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

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + c^{2} y = sec^{2} (c x)

Solve linear ODE:

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

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

y^{^{''}} - 3 y^{^{'}} + 5 y = 4 x^{3} - 2 x

y^{^{''}} - 8 y^{^{'}} + 16 y = 24 x + 2, y (0) = 2, y^{^{'}} (0) = - 1

y^{^{'''}} + y^{^{''}} - 5 y^{^{'}} + 3 y = e^{- t} + sin (t)

\frac{d ^{2} y}{d x ^{2}} + 100 y = 1000 sin (10 x)

y^{^{''}} - 2 y^{^{'}} + y = 4 x^{2} - 3 + x^{- 1} e^{x}