12nd one is really easy!
take x2+y2=t2
then xdx+ydy=2tdt
and multiply both the sides by x2
we get
2tdt/d(y/x)=√(a2-t2)/(1+(y/x)2)
hence
(2t/√a2-t2)dt=d(y/x)/(1+(y/x)2)
put √a2-t2=z
integrating we have
-2√z=tan-1(y/x)+c
solve the differential equations
Q 1... x(x-y) dy + y2 dx= 0
Q2 ... (x dx + y dy)/(x dy - y dx)= √(a2-x2-y2)/(x2+y2)
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UP 0 DOWN 0 0 3
3 Answers
1Answer q1.
dy/dx= -y2/x(x-y)
Take y=vx
dy/dx=v+x.dv/dx
v+x.dv/dx=-v2/(v-1)
xdv/dx=v/v-1
dx/x=(v-1)/v dv
integrating on both sides
lnx=v-lnv
substituting v=y/x
lnx=y/x -lny+lnx
lny=y/x ........................(answer)
11Nicely Done Rohan... I was doing the same but got stuck in between..
Anyway well done pal...
