Let x = x(y) be the solution of the differential equation 2y e^(x/y²)dx + (y² - 4x e^(x/y²))dy = 0 such that x(1) = 0. Then, x(e) is equal to:

Differential Equations: JEE Main 2022 Mathematics question

JEE Main 2022 · 28 Jun, Evening shift · Q3621

JEE Main 202228 Jun, Evening shiftMathematicsMediumDifferential Equations163× since 2002

Let x = x(y) be the solution of the differential equation

2y\,{e^{x/{y^2}}}dx + \left( {{y^2} - 4x{e^{x/{y^2}}}} \right)dy = 0

such that x(1) = 0. Then, x(e) is equal to :

JEE Main 2022 · 28 Jun, Evening shift · Q3621

JEE Main 202228 Jun, Evening shiftMathematicsMediumDifferential Equations163× since 2002

Let x = x(y) be the solution of the differential equation

2y\,{e^{x/{y^2}}}dx + \left( {{y^2} - 4x{e^{x/{y^2}}}} \right)dy = 0

such that x(1) = 0. Then, x(e) is equal to :