# how do I get F(y/x)?

#### PG1995

Joined Apr 15, 2011
832
Hi

As you can see, the book gives two formulas to solve homogeneous equation: Formulas.

Regards
PG

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#### steveb

Joined Jul 3, 2008
2,436
Hi

As you can see, the book gives two formulas to solve homogeneous equation: Formulas.

Regards
PG
When you have a ratio of two things, you can multiply both that top and the bottom by the same quantity and maintain the equality. Think about what you can multiply (or divide) the top and bottom by to get it in the correct form.

#### PG1995

Joined Apr 15, 2011
832
Hi Steve

Please check if I'm doing it right. Thanks a lot for being there to help me.

With best wishes
PG

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#### steveb

Joined Jul 3, 2008
2,436
Hi Steve

Please check if I'm doing it right. Thanks a lot for being there to help me.

With best wishes
PG
I agree with everything but you last step L8. Just double check that and see if you made an algebraic mistake there.

#### PG1995

Joined Apr 15, 2011
832
Thank you.

You are right I made an error which might look trivial in itself but made the end result wrong. In L7 I had In(x) but while doing a calculation on the equation of L7 I instead wrote In(|x|) which is responsible for the error. I believe the correct solution is:

$$\ln x-2\ln \left\vert x\right\vert +2\ln \left\vert x+y\right\vert -\frac{1}{x}y+c=0$$

Please check it. Thank you very much.

Best wishes
PG

Last edited:

#### PG1995

Joined Apr 15, 2011
832
Hi

As you can see here, there are two formulae given for homogeneous equation, 18.5 and 18.6. The form of the homogeneous differential equation I have encountered often so far is the 18.5 one. I see for 18.6 form, we have to take v=xy instead of v=y/x as was the case for the 18.5. I was searching for some example problem which uses the formula 18.6 but wasn't successful. Could you please help? Thanks.

Best wishes
PG