It looks simple, but I can’t do it

[tomcenjerrym]

Can anyone help me how to make the following equation each variable x and y together with dx and dy respectively?

y'=\frac {(4x^2 + y^2)} {xy}

Thanks in advance

 

[Xevarion]

Try letting z=y/x and creating a differential equation for z using the one for y.

 

[HallsofIvy]

Can anyone help me how to make the following equation each variable x and y together with dx and dy respectively?

y'=\frac {(4x^2 + y^2)} {xy}

Thanks in advance

y'= dy/dx so this is
\frac{dy}{dx}= \frac{4x^2+ y^2}{xy}
xydy= (4x^2+ y^2)dx
-(4x^2+y^2)dx+ xydy= 0
Is that what you meant?

You could also let v= y/x and make the substitution y= xv. In that case, dy= xdv+ vdx and the equation becomes
(-4x^2+ x^2v^2)dx+ x(vx)(xdv+ vdx)= 0[/itex]<br /> x^2(v^2- 4)dx+ x^2vdv+ x^2v^2dx= 0[/itex]&lt;br /&gt; x^2(2v^2-4)dx+ x^2vdv= 0[/itex]&amp;lt;br /&amp;gt; As long as x is not 0 we can divide by x^2&amp;lt;br /&amp;gt; (2v^2-4)dx+ vdv= 0&amp;lt;br /&amp;gt; dx+ \frac{v}{2v^2- 4}dv= 0&amp;lt;br /&amp;gt; Is that what you mean?