The integrating factor of the differential equation (1- ...

CBSE Class 12 Math 2023 All Sets Solved Paper

Question : 3 of 20

Marks: +1, -0

The integrating factor of the differential equation

(1- y^2)dx\/dy+ yx = ay,

(-1 < y < 1) is

Solution:

Given differential equation is

(1-y^2)\;{dx}/{dy} + yx = ay,(-1 < y < 1)

⇒ \;{dx}/{dy}+\;{yx}/{1-y^2}=\;{ay}/{1-y^2}

⇒ \;{dx}/{dy} + (\;{y}/{1-y^2})x = \;{ay}/{1-y^2}

The given equation in form of

\;{dx}/{dy} + px = q

∴ I.F. =e^{∫ p d y}

=e^{∫ (\;{y}/{1-y^{2}}) d y}

=e^{∫-\;{1}/{2} (\;{-2 y}/{1-y^{2}}) d y}

=e^{-\;{1}/{2} \log (1-y^{2}) }

=e^{\log \;{1}/{√{1-y^{2}}}}

∴ I.F. =\;{1}/{√{1-y^{2}}}

Go to Question:

Prev Question

Next Question