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Differential Equations question

2023 · 25 Jan · Shift 1 · Q37

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JEE Main
Mathematics
Differential Equations
2023 · 25 Jan · Shift 1 · Q37

Differential Equations question

2023 · 25 Jan · Shift 1 · Q37

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let

y = y(x)

be the solution curve of the differential equation

{{dy} \over {dx}} = {y \over x}\left( {1 + x{y^2}(1 + {{\log }_e}x)} \right),x \gt 0,y(1) = 3

. Then

{{{y^2}(x)} \over 9}

is equal to :

A
${{{x^2}} \over {5 - 2{x^3}(2 + {{\log }_e}{x^3})}}$
B
${{{x^2}} \over {3{x^3}(1 + {{\log }_e}{x^2}) - 2}}$
C
${{{x^2}} \over {7 - 3{x^3}(2 + {{\log }_e}{x^2})}}$
D
${{{x^2}} \over {2{x^3}(2 + {{\log }_e}{x^3}) - 3}}$

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