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

Asked by Sakshi | 1 year ago |  65

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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