(cos(x)sin(x)-xy^2)dx+y(1-x^2)dy=0

解答

(cos (x) sin (x) - x y^{2}) d x + y (1 - x^{2}) d y = 0

y = \frac{- cos ( 2 x ) - c _{1}}{2 ( x + 1 ) ( x - 1 )}, y = - \frac{- cos ( 2 x ) - c _{1}}{2 ( x + 1 ) ( x - 1 )}

求解步骤

(cos (x) sin (x) - x y^{2}) d x + y (1 - x^{2}) d y = 0

求解贝努力方程:

y = \frac{- cos ( 2 x ) - c _{1}}{2 ( x + 1 ) ( x - 1 )}, y = - \frac{- cos ( 2 x ) - c _{1}}{2 ( x + 1 ) ( x - 1 )}

y = \frac{- cos ( 2 x ) - c _{1}}{2 ( x + 1 ) ( x - 1 )}, y = - \frac{- cos ( 2 x ) - c _{1}}{2 ( x + 1 ) ( x - 1 )}

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