If the curve $y = y(x)$ is the solution of the differential equation $2({x^2} + {x^{5/4}})dy - y(x + {x^{1/4}}){\rm{ }}dx = 2{x^{9/4}}dx,\,\,x > 0$ which passes through the point $\left( {1,\,\,1 - \frac{4}{3}{{\log }_e}2} \right)$,then the value of $y(16)$ is equal to

JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

1 Easy

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Analyzing +4 | -1

If the curve

y = y(x)

is the solution of the differential equation

2({x^2} + {x^{5/4}})dy - y(x + {x^{1/4}})\mathrm{ }dx = 2{x^{9/4}}dx,\,\,x > 0

which passes through the point

\left( {1,\,\,1 - \frac{4}{3}{{\log }_e}2} \right)

,then the value of

y(16)

is equal to

View answer and explanation

Correct option: C

4\left( {\frac{{31}}{3} - \frac{8}{3}{{\log }_e}3} \right)

Option C (

4\left( {\frac{{31}}{3} - \frac{8}{3}{{{\log }_e}3} \right)

) is correct because it is the result of solving the given differential equation and applying the provided initial condition to find y(16).