Differential Equation Solution and Value (Jee M…

First Order Differential Equations

Hard

Differential Equation Solution and Value

Let y = y(x) be the solution of the differential equation $\frac{{dy}}{{dx}}$ +2y sec² x = 2sec²x + 3tan x.sec²x such that y(0) = $\frac{5}{4}$ . Then $12\left( {y\left( {\frac{\pi }{4}} \right)-{e^{-2}}} \right)$ is equal to __________.

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