The solution of the differential equation dy/dx + 2yx/1+x² = 1/(1+x²)² is

Correct Answer is : y (1 + x2x²x2) = C + tan⁡−1^{-1}tan−1 x

Correct Answer is : y (1 + x2x²x2) = C + tan⁡−1^{-1}tan−1 x

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VITEEE 2012 Paper

Section: Mathematics

Question : 81 of 120

Marks: +1, -0

\frac{dy}{dx}

\frac{2yx}{1+x^2}

\frac{1}{(1+x^2)^2}

Solution:

\frac{dy}{dx}

\frac{2yx}{1+x^2}

\frac{1}{(1+x^2)^2}

which is a linear differential equation

Here, P =

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

, Q =

\frac{1}{(1+x^2)^2}

Now, IF =

e^{\int P dx}

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

e^{\log(1+x^2)}

(1+x^2)

∴ Solution of differential equation is

y .

(1+x^2)

= ∫

\frac{1}{(1+x^2)^2}

. (1 +

x^2

) dx + C

⇒ y (1 +

x^2

) = ∫

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

dx + C

⇒ y (1 +

x^2

) = C +

\tan^{-1}

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