- #1
Adrynalyne
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Homework Statement
Solve the given differential equation by using an appropriate substitution.
Homework Equations
[tex](x^{2}+xy+3y^{2})dx-(x^{2}+2xy)dy=0[/tex]
[tex]y=ux, dy=udx+xdu[/tex]
The Attempt at a Solution
[tex](x^{2}dx+ux^{2}dx+3u^{2}x^{2}dx)-(ux^{2}dx+x^{3}du+2u^{2}x^{2}dx+2ux^{3}du)=0[/tex]
After combining, cancelling and moving terms into their appropriate places, I get:
[tex]\frac{dx}{x}=\frac{2u+1}{u^{2}+1}du[/tex]
This is where I get stuck, I am unable to integrate the right hand side. Can anyone help me out a little?
Thanks.