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Differential Equations question

2024 · 30 Jan · Shift 1 · Q52

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JEE Main
Mathematics
Differential Equations
2024 · 30 Jan · Shift 1 · Q52

Differential Equations question

2024 · 30 Jan · Shift 1 · Q52

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

Let

y=y(x)

be the solution of the differential equation

\left(1-x^2\right) \mathrm{d} y=\left[x y+\left(x^3+2\right) \sqrt{3\left(1-x^2\right)}\right] \mathrm{d} x, -1\lt x\lt 1, y(0)=0

. If

y\left(\frac{1}{2}\right)=\frac{\mathrm{m}}{\mathrm{n}}, \mathrm{m}

and

\mathrm{n}

are co-prime numbers, then

\mathrm{m}+\mathrm{n}

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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