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dy+7xdx=0

解答

d y + 7 x d x = 0

解答

y = - \frac{7 x ^{2}}{2} + c_{1}

求解步骤

d y + 7 x d x = 0

令

y

为因变量。除以

d x

:

\frac{d y}{d x} + 7 x = 0

用

y^{'} (x)

替代

\frac{d y}{d x}

y^{^{'}} (x) + 7 x = 0

整理

y^{'} (x) : y^{'} (x) = - 7 x

若

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

则

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

y = \int - 7 x d x

\int - 7 x d x = - \frac{7 x ^{2}}{2} + c_{1}

y = - \frac{7 x ^{2}}{2} + c_{1}

作图

流行的例子

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\frac{d}{d x} (- \frac{2}{( 1 + x ) ^{3}})

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x \to 3 lim (\frac{( 3 - x )}{x - 3})

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x \to 8 lim (\frac{x + 8}{x - 8})