x(dy)/(dx)+y=sec(xy)

解答

x \frac{d y}{d x} + y = sec (x y)

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

求解步骤

x \frac{d y}{d x} + y = sec (x y)

使用替代法求解:

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

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

\frac{d}{d x} (2 x e^{x + 3} + e^{x + 3} x^{2})

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n = 0 \sum \infty (\frac{- 1}{3})^{2 n}

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