y-x dy/dx=a(y 2 +dy/dx)

y-x dy/dx=a(y2+dy/dx)


2 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

Dear upendra

y-x dy/dx=a(y2+dy/dx)

dy/dx (a+x)=y-ay2

dy/(y-ay2) =dx/(a+x)

intigrate both side

∫dy/(y-ay2) =∫dx/(a+x)

∫{1/y    + a/(1-ay) }dy =∫dx/(a+x)

ln|y| -ln|1-ay| +c=ln|x+a|

  ln(x+a)(1-ay)/y   =c


or (x+a)(1-ay)/y   =C1

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Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the solution to your problem.
y – xdy/dx = a(y2+dy/dx)
dy/dx (a+x) = y – ay2
dy/(y – ay2) =dx/(a+x)
intigrate both side
∫dy/(y – ay2) =∫dx/(a+x)
∫{1/y + a/(1 – ay)}dy = ∫dx/(a + x)
ln|y| – ln|1 – ay| + c = ln|x + a|
ln(x + a)(1 – ay)/y = c
or (x + a)(1 – ay)/y = C1
Hope it helps.
Thanks and regards,

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