Find the general solution

Find the general solution of the differential equation .

But the answer given in the book is . Where have I gone wrong?

Re: Find the general solution

Re: Find the general solution

Quote:

Originally Posted by

**alexmahone** Find the general solution of the differential equation

.

But the answer given in the book is

. Where have I gone wrong?

You have gone wrong by treating y as a constant and not as a function of x.

You should recognise that this is actually a Bernoulli Equation.

Re: Find the general solution

Quote:

Originally Posted by

**chisigma** Setting

Your DE is...

(1)

... and the integration is immediate...

(2)

Kind regards

But what's wrong with *my* solution?

Re: Find the general solution

Quote:

Originally Posted by

**Prove It** You have gone wrong by treating y as a constant and not as a function of x.

You should recognise that this is actually a Bernoulli Equation.

I know that this is a Bernoulli equation; that is why I multiplied by the integrating factor x. Which step of my solution is actually invalid?

Re: Find the general solution

Quote:

Originally Posted by

**alexmahone** I know that this is a Bernoulli equation; that is why I multiplied by the integrating factor x. Which step of my solution is actually invalid?

Which steps are invalid?

1. Not making an appropriate substitution.

2. Performing integration treating a function of the independent variable like a constant...

Re: Find the general solution

Quote:

Originally Posted by

**alexmahone** But what's wrong with *my* solution?

You arrived [correctly...] to write...

(1)

... and then You [incorrectly...] operated as in case of separate variables... but in (1) x and y *aren't* separate...

Kind regards