Given:
dxdy=2xyx2+y2
Put y=vx⇒dxdy=v+xdxdv
v+xdxdv=2v1+v2
⇒xdxdv=2v1−v2
⇒∫(v2−12v)dv=−∫xdx
⇒loge∣v2−1∣=loge(xC)
⇒x2y2−x2=xC
⇒y2−x2=Cx
Put x=2 and y=0 we get,
0−22=2C⇒C=−2
⇒y2=x2−2x
⇒y(8)=82−16
⇒y(8)=48=43
The slope of tangent at any point (x,y) on a curve y=y(x) is 2xyx2+y2,x>0. If y(2)=0, then a value of y(8) is
Held on 10 Apr 2023 · Verified 6 Jul 2026.
−42
23
−23
43
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