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

Question

If the curve y = y(x) is the solution of the differential equation

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

passes through the point $\left( {1,1 - {4 \over 3}{{\log }_e}2} \right)$, then the value of y(16) is equal to :

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

$\left( {{{31} \over 3} - {8 \over 3}{{\log }_e}3} \right)$

$\left( {{{31} \over 3} + {8 \over 3}{{\log }_e}3} \right)$

$4\left( {{{31} \over 3} + {8 \over 3}{{\log }_e}3} \right)$

Solution

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