Find the particular solution satisfying the given condition $$\dfrac{dy}{dx} +(\dfrac{(1+y^2)}{y}) = 0$$

Asked by Sakshi | 1 year ago |  75

##### Solution :-

From the question it is given that,

$$(\dfrac{dy}{dx}) + \dfrac{1 + y^2}{y} = 0$$

Transposing we get,

$$\dfrac{dy}{dx}= \dfrac{– (1 + y^2)}{y}$$

By cross multiplication,

$$\dfrac{y}{(1 + y^2)}dy = – dx$$

Integrating on both side, we get,

$$∫\dfrac{y}{(1 + y^2)} dy = ∫-dx$$

$$∫\dfrac{2y}{(1 + y^2)} dy = -2 ∫dx$$

log (1 + y2) = – 2x + c1

Therefore,

$$\dfrac{1}{2}log [1 + y^2] + x = c$$

Answered by Aaryan | 1 year ago

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