BITSAT 2015 Paper

Given differential equation is
dy + {y ϕ ' (x) – ϕ (x) ϕ (x)} dx = 0
⇒

dy]

dx

+ ϕ ' (x) y = ϕ (x) ϕ ' (x)
which is a linear differential equation with
P = ϕ ' (x) , Q = ϕ (x) . ϕ ' (x) and
I.F. = e∫ϕ′(x)dx = eϕ(x)
∴ Solution is y. eϕ(x) = ∫ ϕ (x . ϕ ' (x) eϕ(x) dx + C
⇒ y.eϕ(x) = ∫ ϕ

(x)

I

.eϕ(x)ϕ′

(x)

II

dx + C
⇒ y.eϕ(x) = ϕ (x) eϕ(x) - ∫ ϕ ' (x) eϕ(x) dx + C
⇒ y.eϕ(x) = ϕ (x) eϕ(x) - eϕ(x) + C
⇒ y = {ϕ(x)−1} + Ce−ϕ(x)