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**xdy/dx+y=1/y^2:using substitution in differential eq**

## Homework Statement

solve using substitution

xdy/dx+y=1/y^2

## The Attempt at a Solution

Thanks to the people who've help me thus far. here's a bernulli problem that I'm having. I change this problem around to...

dy/dx=y^3/xy^2

xy^2dy=y^3dx

using u sub.

u=y^3

du=3y^2dy

substituted problem

1/3xdu=udx

du/dx=3xu

du/dx-3xu=0

then I get e^(integral -3x)=e^(-3x^2/2)

Here's where I'm stuck

e^(-3x^2/2)u=integral 0*e^(-3x^2/2)

doesn't that just have c? which later becomes

u=ce^(3x^2/2)

However, that's not the solution of the equation which is

y^3=1+cx^-3

Can someone explain why?

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