The expression satisfying the differential equation (x²-1)dy/dx + 2xy = 1 is

Correct Answer is : (x2−1)(x²-1)(x2−1) y = x + c

Correct Answer is : (x2−1)(x²-1)(x2−1) y = x + c

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BITSAT 2018 Paper

Section: Mathematics

Question : 116 of 150

Marks: +1, -0

(x^2-1)\frac{dy}{dx}

+ 2xy = 1 is

Solution:

Rewrite the given differential equation as follows :

\frac{dy}{dx}

\frac{2x}{x^2-1}

y =

\frac{1}{x^2-1}

, which is a linear form

The integrating factor I.F.

e^{\int \frac{2x}{x^2-1} dx}

e^{\ln(x^2-1)}

x^2

- 1

we get

(x^2-1)

\frac{dy}{dx}

+ 2xy = 1

⇒

\frac{d}{dx}

[y(x^2-1)]

= 1

On integrating we get

y(x^2-1)

= x + c

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