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ODE seperable method [Pending...]

My question

(y/x)*(dy/dx)=sqrt(1+x^2+y^2+x^2*y^2)

Relevant page

Differential Equations - Separable Equations

What I've done so far

replaced 1+x^2+y^2+x^2*y^2 with t

X

(y/x)*(dy/dx)=sqrt(1+x^2+y^2+x^2*y^2)
Relevant page

<a href="http://tutorial.math.lamar.edu/Classes/DE/Separable.aspx">Differential Equations - Separable Equations</a>

What I've done so far

replaced 1+x^2+y^2+x^2*y^2 with t

Re: ODE seperable method

Hello Ahmed

You are encouraged to use the Math Input system so your math is easier to read.

Then your question looks like this:

`(y/x)(dy/dx)=sqrt(1+x^2+y^2+x^2*y^2)`

The first hint is to factor the expression under the square root. Do that first, then we'll go from there.

X

Hello Ahmed

You are encouraged to use the <a href="/forum/entering-math-graphs-images-41/how-to-enter-math:91">Math Input system</a> so your math is easier to read.

Then your question looks like this:

`(y/x)(dy/dx)=sqrt(1+x^2+y^2+x^2*y^2)`

The first hint is to factor the expression under the square root. Do that first, then we'll go from there.

Re: ODE seperable method

Ok I've factorised it now it looks like

(y/x)*(dy/dx)=sqrt((x^2+1)(y^2+1))

now what.

X

Ok I've factorised it now it looks like

(y/x)*(dy/dx)=sqrt((x^2+1)(y^2+1))

now what.

Re: ODE seperable method

Putting back ticks around your (correct) answer makes it appear as:

`(y/x)*(dy/dx)=sqrt((x^2+1)(y^2+1))`

OK, now you need to separate the variables. That is, put all the `y` and `dy` parts together on the left, and the `x` and `dx` parts together on the right.

X

Putting back ticks around your (correct) answer makes it appear as:

`(y/x)*(dy/dx)=sqrt((x^2+1)(y^2+1))`

OK, now you need to separate the variables. That is, put all the `y` and `dy` parts together on the left, and the `x` and `dx` parts together on the right.

Re: ODE seperable method

It seems Ahmed has disappeared. Anyone else like to have a go at finishing it?

X

It seems Ahmed has disappeared. Anyone else like to have a go at finishing it?

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