y^{''}+16y=8tan(4x)

Lösung

y^{^{''}} + 16 y = 8 tan (4 x)

y = c_{1} cos (4 x) + c_{2} sin (4 x) + \frac{- 2 cos ( 4 x ) ( ln ( tan ( 4 x ) + sec ( 4 x ) ) - sin ( 4 x ) ) - sin ( 8 x )}{4}

Schritte zur Lösung

y^{''} (x) + 16 y = 8 tan (4 x)

Solve linear ODE:

y = c_{1} cos (4 x) + c_{2} sin (4 x) + \frac{- 2 cos ( 4 x ) ( ln ( tan ( 4 x ) + sec ( 4 x ) ) - sin ( 4 x ) ) - sin ( 8 x )}{4}

y = c_{1} cos (4 x) + c_{2} sin (4 x) + \frac{- 2 cos ( 4 x ) ( ln ( tan ( 4 x ) + sec ( 4 x ) ) - sin ( 4 x ) ) - sin ( 8 x )}{4}

\frac{2 y ^{^{'}}}{y} = x

\int \frac{2 x ^{3} - 4 x ^{2} - x - 3}{x ^{2} - 2 x - 3} d x

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

x \to 0 lim (\frac{e ^{x} - 1}{x})

d er i v a t i v e y = 3 x^{2} + 5 x - 1