展开 (e^{x^2}y= 1/2 e^{x^2}+c) 1/(e^{x^2)}

解答

展开

(e^{x^{2}} y = \frac{1}{2} e^{x^{2}} + c) \frac{1}{e ^{x^{2}}}

y = \frac{1}{2} e^{x^{2}} + \frac{c}{e ^{x^{2}}}

求解步骤

(e^{x^{2}} y = \frac{1}{2} e^{x^{2}} + c) \frac{1}{e ^{x^{2}}}

= \frac{1}{e ^{x^{2}}} (\frac{1}{2} = e^{x^{2}} e^{x^{2}} y + c)

使用分配律:

a (b + c) = ab + a c

a = \frac{1}{e ^{x^{2}}}, b = e^{x^{2}} y = \frac{1}{2} e^{x^{2}}, c = c

\frac{1}{e ^{x^{2}}} e^{x^{2}} y = \frac{1}{2} e^{x^{2}} + \frac{1}{e ^{x^{2}}} c

e^{x^{2}} \frac{1}{e ^{x^{2}}} y = \frac{1}{2} e^{x^{2}} + c \frac{1}{e ^{x^{2}}}

化简

e^{x^{2}} \frac{1}{e ^{x^{2}}} y = \frac{1}{2} e^{x^{2}} + c \frac{1}{e ^{x^{2}}} : y = \frac{1}{2} e^{x^{2}} + \frac{c}{e ^{x^{2}}}

y = \frac{1}{2} e^{x^{2}} + \frac{c}{e ^{x^{2}}}

e x p an d \frac{3 ( 7 4 ^{\frac{2}{3}} - 5 7 ^{\frac{2}{3}} )}{4}

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