dy/dx=a+b/y a.b为常数 ,求y=f(x)=?
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dy/dx=a+b/y a.b为常数 ,求y=f(x)=?

本题积分结果为:

y = ax + (b/a) ln (ay + b) + C

验证:

dy/dx = a + (b/a) [1 / (ay+b)]*a*dy/dx

dy/dx = a + [ b / (ay+b) ] dy/dx

dy/dx [1 - b / (ay+b) ] = a

dy/dx [ay / (ay + b)] =a

dy/dx = a(ay + b) / (ay) = a + b / y

结果正确.