y-x dy/dx=a(y2+dy/dx)
y-x dy/dx=a(y2+dy/dx)
upendra hembram , 16 Years ago
Grade 12
Differential Calculus> differential equation...
2 Answers
Badiuddin askIITians.ismu Expert
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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Badiuddin
Kushagra Madhukar
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,
Kushagra
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