(d^2y)/(dx^2)+4y=tan(2x)

Lösung

\frac{d ^{2} y}{d x ^{2}} + 4 y = tan (2 x)

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

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + 4 y = tan (2 x)

Solve linear ODE:

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

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

y^{^{''''}} + 2 y^{^{''}} + 1 = 0

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

y^{^{''}} - 2 y^{^{'}} + y = \frac{3 e ^{t}}{1 + t ^{2}}

y^{^{''}} + y = 4 x + 10 sin (x), y (π) = 0, y^{^{'}} (π) = 2

9 y^{^{''}} - 6 y^{^{'}} + y = cos (t)