Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
x2dy = (2xy + y2)dx
Substituting in (i), we get
integrating both sides
`=>y/(y+x)=Cx` [Removing logarithm in both sides]
`therefore y=Cxy+Cx^2` ,which is the general solution.
Putting y=1 and x=1,
`1=C + C`
`therefore 2y=xy+x^2,` which is the particular solution.
Concept: Methods of Integration: Integration by Substitution
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