2xsin(3y)dx+3x^2cos(3y)dy=0

解答

2 x sin (3 y) d x + 3 x^{2} cos (3 y) d y = 0

y = \frac{arcsin ( \frac{c _{1}}{x ^{2}} )}{3} + \frac{2 πn}{3}, y = \frac{π}{3} + \frac{arcsin ( - \frac{c _{1}}{x ^{2}} )}{3} + \frac{2 πn}{3}

求解步骤

2 x sin (3 y) d x + 3 x^{2} cos (3 y) d y = 0

求解可分离方程:

y = \frac{arcsin ( \frac{c _{1}}{x ^{2}} )}{3} + \frac{2 πn}{3}, y = \frac{π}{3} + \frac{arcsin ( - \frac{c _{1}}{x ^{2}} )}{3} + \frac{2 πn}{3}

y = \frac{arcsin ( \frac{c _{1}}{x ^{2}} )}{3} + \frac{2 πn}{3}, y = \frac{π}{3} + \frac{arcsin ( - \frac{c _{1}}{x ^{2}} )}{3} + \frac{2 πn}{3}

(x sin (y)) \frac{d y}{d x} = 1 + 2 x^{2}

0.001 \cdot y^{^{'}} + 0.001 \cdot y = 0

y^{^{'}} = - a y x

y^{^{'}} = 9 x^{8} y

(x^{3} + 1) \cdot y^{^{'}} - (3 \cdot x^{2}) \cdot y = 0