CBSE Class 12-science Answered
Find the general solution of the following differential equation
Asked by pratikbharadia | 30 Dec, 2009, 11:49: AM
Expert Answer
dy/dx = -y/(2(xy) - x )
Put y = vx
Therefore, dy/dx = v + xdv/dx
v + xdv/dx = -vx/(2(vx2) - x )
v + xdv/dx = -vx/(2xv - x )
v + xdv/dx = -v/(2v - 1 )
xdv/dx = [-v/(2v - 1 )] - v
xdv/dx = -2vv/(2v - 1)
Separating the variables,
(2v - 1)dv/(-2vv) = dx/x
Put 2v - 1 = z, and dv/v = dz
- 2zdz/(1+z)2 = dx/x
Integrating both sides, by parts on LHS,
-2(-z/(1+z) + dz/(1+z)) = log x
2z/(1+z) -2log (1+z) = log x
2z/(1+z) = log (x(1+z)2)
Hence the solution is,
(2(y/x) - 1)/(y/x) = log 4y
Regards,
Team,
TopperLearning.
Answered by | 31 Dec, 2009, 12:29: PM
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