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The integrating factor of equation sec 2 y dy/dx + x tan y = x3 is

a) $[e]^{x^2/2}$

b) $[e]^ {-x^2/2}$

c) $[e]^{x/2}$

d)$ [e]^{-x/2}$
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Anser is apsan  b
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Put $tany = t$

and by differentiating both sides we get,

$sec^2y dy= dt$ --------(1)

Now put (1) in the given differential euation,

$\frac{\mathrm{d} t}{\mathrm{d} x} + x*t = x^{3}$              --------------> Linear Differential Equation

Integrating factor => IF=$e^{\int xdx}$ = $e^{\tfrac{x^2}{2}}$
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