Some double angle identity to solve (2x^{2}+y^{2}) \frac{dy}{dx}=2xy?

veksetz 2022-01-20 Answered
Some double angle identity to solve (2x2+y2)dydx=2xy?
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Expert Answer

Mary Herrera
Answered 2022-01-20 Author has 37 answers
If we write the equation as,
dydx=2xy2x2+y2
and then divide through x2 we will get:
dydx=2yx2+(yx)2
This suggests that we simplify the previous equation in terms of
f(v)=2v2+v2
So putting
yx=v
y=vx
y=vx+v
We get
dvdxx+v=2v2+v2
Then
dvdxx=v32+v2
dxx=2+v2v3dv
dxx=(2v31v)dv
Upon integration we have:
logx+C=1v2logv
Lets

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Elaine Verrett
Answered 2022-01-21 Author has 41 answers
Rewrite equation into form :
dydx=2xy2x2+y2
Substitute:
z=yxy=xz+z
Therefore:
xz+z=frac2z2+z2Rightarrowxz=z32+z22+z2z3dz=dxx

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