展开 (1/y)((e^x+y^2)dx+(xy-(e^x)/y-2y^2)dy=0)

解答

展开

(\frac{1}{y}) ((e^{x} + y^{2}) d x + (x y - \frac{e ^{x}}{y} - 2 y^{2}) d y = 0)

\frac{e ^{x} d x}{y} + y d x + x d y - \frac{e ^{x} d y}{y ^{2}} - 2 y d y = 0

求解步骤

(\frac{1}{y}) ((e^{x} + y^{2}) d x + (x y - \frac{e ^{x}}{y} - 2 y^{2}) d y = 0)

= (\frac{1}{y}) ((e^{x} + y^{2}) d x + 0 = (y x - \frac{e ^{x}}{y} - 2 y^{2}) d y)

使用分配律:

a (b + c) = ab + a c

a = (\frac{1}{y}), b = (e^{x} + y^{2}) d x, c = (x y - \frac{e ^{x}}{y} - 2 y^{2}) d y = 0

(\frac{1}{y}) (e^{x} + y^{2}) d x + (\frac{1}{y}) (x y - \frac{e ^{x}}{y} - 2 y^{2}) d y = 0

(\frac{1}{y}) (e^{x} + y^{2}) d x + (\frac{1}{y}) (y x - \frac{e ^{x}}{y} - 2 y^{2}) d y = 0

乘开

(\frac{1}{y}) (e^{x} + y^{2}) d x + (\frac{1}{y}) (y x - \frac{e ^{x}}{y} - 2 y^{2}) d y : \frac{e ^{x} d x}{y} + y d x + x d y - \frac{e ^{x} d y}{y ^{2}} - 2 y d y

\frac{e ^{x} d x}{y} + y d x + x d y - \frac{e ^{x} d y}{y ^{2}} - 2 y d y = 0

s im pl i f y 127 \cdot (1 - \frac{1}{( 1 + 0.16 ) ^{10.5}})

e x p an d - \frac{4}{( x ^{2} - 1 ) ^{2}}

e x p an d - \frac{( x - 6 ) ^{2}}{12}

e x p an d (e^{x} + ln (y) + \frac{y}{x}) d x

e x p an d sec (x) (1 - cos (x) = sec (x) - 1)