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(2x-1)dx+(3x+7)dy=0

解答

(2 x - 1) d x + (3 x + 7) d y = 0

解答

y = - \frac{2}{3} x + \frac{17}{9} ln (3 x + 7) + c_{1}

求解步骤

(2 x - 1) d x + (3 x + 7) d y = 0

令

y

为因变量。除以

d x

:

2 x - 1 + (3 x + 7) \frac{d y}{d x} = 0

用

y^{'} (x)

替代

\frac{d y}{d x}

2 x - 1 + (3 x + 7) y^{^{'}} (x) = 0

整理

y^{'} (x) : y^{'} (x) = \frac{- 2 x + 1}{3 x + 7}

若

f^{^{'}} (x) = g (x)

则

f (x) = \int g (x) d x

y = \int \frac{- 2 x + 1}{3 x + 7} d x

\int \frac{- 2 x + 1}{3 x + 7} d x = - \frac{2}{3} x + \frac{17}{9} ln (3 x + 7) + c_{1}

y = - \frac{2}{3} x + \frac{17}{9} ln (3 x + 7) + c_{1}

作图

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