The integrating factor of the differential equation $\left(1-y^{2}\right)\dfrac{dx}{dy}+yx=ay,\ (-1<y<1)$ is:

(D) $\dfrac{1}{\sqrt{1-y^{2}}}$

(B) $\dfrac{1}{\sqrt{y^{2}-1}}$

CBSE Class 12 · 2023 · Differential EquationsMultiple Choice

The integrating factor of the differential equation

(1 - y^{2}) \frac{d x}{d y} + y x = a y, (- 1 < y < 1)

is:

Answer: (D)

Write it as a linear equation in

x

(with

y

independent):

\frac{d x}{d y} + \frac{y}{1 - y ^{2}} x = \frac{a y}{1 - y ^{2}}

Here

P = \frac{y}{1 - y ^{2}}

, so

I.F. = e^{\int \frac{y}{1 - y ^{2}} d y} = e^{- \frac{1}{2} l o g (1 - y^{2})} = \frac{1}{1 - y ^{2}}

I.F. = \frac{1}{1 - y ^{2}}

CBSE Class 12 Board · 2023 · Single correct option