Find the particular solution satisfying the given condition xy (y + 1)dy = (x2 + 1) dx

Asked by Sakshi | 1 year ago |  35

1 Answer

Solution :-

From the question it is given that,

xy (y + 1)dy = (x2 + 1) dx

By cross multiplication,

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

(y2 + y)dy =$$x + (\dfrac{1}{x})dx$$

Integrating on both side, we get,

∫(y2 + y)dy = ∫(x + ($$\dfrac{1}{x}$$)) dx

$$(\dfrac{y^3}{3}) + (\dfrac{y^2}{2}) = (\dfrac{x^2}{2}) + log x + c$$

Answered by Aaryan | 1 year ago

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