求方程dy/dx=(e^y+3x)/x^2的通解.

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求方程dy/dx=(e^y+3x)/x^2的通解.求方程dy/dx=(e^y+3x)/x^2的通解.求方程dy/dx=(e^y+3x)/x^2的通解.令dy1/dx=e^y1/x^2,dy2/dx=3

求方程dy/dx=(e^y+3x)/x^2的通解.
求方程dy/dx=(e^y+3x)/x^2的通解.

求方程dy/dx=(e^y+3x)/x^2的通解.

dy1/dx=e^y1/x^2,
dy2/dx=3x/x^2=3/x,
1)解y1
e^(-y1)dy1 = (1/x^2)dx
积分得
-e^(-y1) = -1/x
y1 = -ln |1/x|
2)解y2
dy2 = (3/x)dx
积分得
y2 = 3ln |x|
则y=y1+y2 +C
= 3ln |x| -ln |1/x | +C