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Differential Equations question

2025 · Shift 2 · Q25

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JEE Advanced
Mathematics
Differential Equations
2025 · Shift 2 · Q25

Differential Equations question

2025 · Shift 2 · Q25

JEE AdvancedMathematicsDifferential EquationsNumerical+4 / −1

Let

y(x)

be the solution of the differential equation

x^2 \frac{d y}{d x}+x y=x^2+y^2, \quad x\gt \frac{1}{e}

satisfying

y(1)=0

. Then the value of

2 \frac{(y(e))^2}{y\left(e^2\right)}

is

\underline{\hspace{2cm}}

.

Numerical answer

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