The solution of differential equation $\frac{{dt}}{{dx}} = \frac{{t\left( {\frac{d}{{dx}}\left( {{\rm{g}}\left( x \right)} \right)} \right) - {t^2}}}{{{\rm{g}}\left( x \right)}}$ is

$t = \frac{{{\rm{g}}\left( x \right)}}{{x + c}}$

$t = \frac{{{\rm{g}}\left( x \right) + c}}{x}$

$t = \frac{{{\rm{g}}\left( x \right)}}{x} + c$

$t = {\rm{g}}\left( x \right) + x + c$

JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

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Application +4 | -1

The solution of differential equation

\frac{{dt}}{{dx}} = \frac{{t\left( {\frac{d}{{dx}}\left( {\mathrm{g}\left( x \right)} \right)} \right) - {t^2}}}{{\mathrm{g}\left( x \right)}}

View answer and explanation

Correct option: C

t = \frac{{\mathrm{g}\left( x \right)}}{{x + c}}

Option D (

t = \frac{{\mathrm{g}\left( x \right)}}}{{x + c}}

) is correct because it is the solution to the given differential equation after applying a suitable substitution and integrating factor.