# Implicit and explicit solution for a given initial-value problem

1. Sep 25, 2011

### Cheruby

The equation is:
x2 dy/dx= y - xy
IC (initial conditions): y(-1) = -1 (This is used to solve for C)
Must first separate the variables x and y and then integrate them and solve for y, but I got stuck...

x2dy = (y - xy)dx
x2dy = y(1-x)dx
dy= y(1-x)dx/x2 <-- not sure what to do with the y now... I figure I could divide everything by y so I could bring it to the left side but the right side would have dx/y

The answer is y = e-(1+1/x)/x

Last edited: Sep 25, 2011
2. Sep 25, 2011

### Jackx

You are doing it right, but when you divide by Y you will have dy/y, and that is perfectly acceptable. The right side you will have (1-x)/x^2 dx. Then integrate both sides.

3. Sep 25, 2011

### Cheruby

But wouldn't the right side have dx/y? That's why i'm stuck, I'm not sure if it's acceptable!

4. Sep 25, 2011

### Jackx

dx can be treated as just another factor on the right side. So since they are all factors when you divide by y the y just goes away on the right side.

Now if it was y + (whatever)dx, then yes if you divided by y you would have a dx/y.

5. Sep 25, 2011

### Cheruby

Alright thank you Jackx

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