JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

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Application +4 | -1

Solution of the equation

x d y=\left(y+x \frac{f\left(\frac{y}{x}\right)}{f^{\prime}\left(\frac{y}{x}\right)}\right) d x

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Correct option: C

f\left(\frac{y}{x}\right)=c x

Option C,

f\left(\frac{y}{x}\right)=c x

, is the correct solution obtained by solving the given homogeneous differential equation using substitution and integration.

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\lim \limits_{{x \rightarrow \infty}} y(t)