PYQ Vault
EbooksTutor

dy/dx + k sec^2 x y = sec^2 x (a + b tan x): find y at a point

The same question, asked 2 times: 2 Apr 2025*, 3 Apr 2025. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2 Apr 2025

    146
    Let y=y(x)y = y(x) be the solution of the differential equation dydx+2ysec⁡2x=2sec⁡2x+3tan⁡x⋅sec⁡2x\frac{dy}{dx} + 2y\sec^{2}x = 2\sec^{2}x + 3\tan x \cdot \sec^{2}x such that y(0)=54y(0) = \frac{5}{4}. Then 12(y(π4)−e−2)12\left( y\left( \frac{\pi}{4} \right) - e^{- 2} \right) is equal to

  2. Question 2

    3 Apr 2025

    139
    Let y=y(x)y=y\left( x \right) be the solution of the differential equation dydx+3(tan⁡2x)y+3y=\frac{dy}{dx}+ 3\left( \tan^{2}x \right)y+ 3y= sec⁡2x\sec^{2}x, y(0)=13+e3y(0) =\frac{1}{3}+e^{3}. Then y(π4)y\left( \frac{\pi}{4} \right) is equal to.

    Tap an option to check your answer.