(dy)/(dx)y=(csc(x)+cot(x))^{-1}

解答

\frac{d y}{d x} y = (csc (x) + cot (x))^{- 1}

y = 2 ln (sec^{2} (\frac{x}{2})) + c_{1}, y = - 2 ln (sec^{2} (\frac{x}{2})) + c_{1}

求解步骤

\frac{d y}{d x} y = (csc (x) + cot (x))^{- 1}

求解可分离方程:

y = 2 ln (sec^{2} (\frac{x}{2})) + c_{1}, y = - 2 ln (sec^{2} (\frac{x}{2})) + c_{1}

y = 2 ln (sec^{2} (\frac{x}{2})) + c_{1}, y = - 2 ln (sec^{2} (\frac{x}{2})) + c_{1}

y^{^{'}} = \frac{y}{x}, y (1) = 1

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

y^{^{'}} = e^{4 y + 4 x}, y (0) = 9

y^{^{'}} = \frac{x ^{2} + 3 x}{2 x y}

(x y + 2 y + x + 2) d y - (x^{2} - 4) d x = 0