Question

If y(x) satisfies the differential equation y' – y tan x = 2x sec x and y(0) = 0, then

Answer 1

Answer is (d) 

Explanation: 

The given differential equation is

y' – y tan x = 2x sec x

(dy/dx) – tan x.y = 2x sec x 

which is a linear differential equation

Thus, IF = e^{–∫tan x dx} = e^{log cos x} = cos x

Hence, the solution is

y.cos x = ∫2x.sec x.cos x dx + c

y.cos x = ∫2x.dx + c

y.cos x = x² + c

when x = 0, y = 0, then c = 0

Thus, the equation of the curve is

y.cos x = x² 

When x = π/4, then y.1/√2 = π²/16