solve this: x^2(xdx+ydy) +2y(xdy-ydx) =0
Answer (1)
17th Feb, 2020
Hello Prathik,
Hope everything going well.
Here is a method from which you can solve such equation:
Multiplying by 2x/x^2
2(xdx+ydy)+4y(xdy−ydx)/x^2=0
d(x^2+y^2)+4yd(y/x)=0
Converting to polar co ordinates
d(r^2)+4rsinθd(tanθ)=0
2rdr+4rsinθsec^2(θ)dθ=0
2rdr+4rsinθsec^2(θ)dθ=0
dr+2secθtanθdθ=0
Integrating,
r+2secθ=C
√( x^2+y^2)+2 √( 1+tan^2(θ))=C
√( x^2+y^2)+2 √( 1+(y^2/x^2))=C
(x+2) √(x^2+y^2)=Cx
Hope this helps you. Thank you.
All the best!!
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