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Differential Equations question

2025 · 7 Apr · Shift 1 · Q32

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JEE Main
Mathematics
Differential Equations
2025 · 7 Apr · Shift 1 · Q32

Differential Equations question

2025 · 7 Apr · Shift 1 · Q32

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

Let

y=y(x)

be the solution curve of the differential equation

x\left(x^2+e^x\right) d y+\left(\mathrm{e}^x(x-2) y-x^3\right) \mathrm{d} x=0, x\gt 0

, passing through the point

(1,0)

. Then

y(2)

is equal to :

A
$\frac{2}{2+e^2}$
B
$\frac{4}{4-e^2}$
C
$\frac{4}{4+e^2}$
D
$\frac{2}{2-e^2}$

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