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Differential Equations question

2021 · 17 Mar · Shift 2 · Q26

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JEE Main
Mathematics
Differential Equations
2021 · 17 Mar · Shift 2 · Q26

Differential Equations question

2021 · 17 Mar · Shift 2 · Q26

JEE MainMathematicsDifferential EquationsMCQ+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}})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 :

A
$4\left( {{{31} \over 3} - {8 \over 3}{{\log }_e}3} \right)$
B
$\left( {{{31} \over 3} - {8 \over 3}{{\log }_e}3} \right)$
C
$\left( {{{31} \over 3} + {8 \over 3}{{\log }_e}3} \right)$
D
$4\left( {{{31} \over 3} + {8 \over 3}{{\log }_e}3} \right)$

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