Question

JEE Mains Maths question is in the image

Answer 1

see ur answer is in attachment

Answer 2

It has given that, y² + ln cos²x = y

we check which of the following is correct.

1. y"(0) = 2
2. |y'(0) + y"(0)| = 3
3. |y'(0) ( y"(0) | = 1
4. none of these

solution : y² + ln cos²x = y

differentiating w.r.t x

2yy' + 1/cos²x × (-2cosx sinx) = y'

⇒2yy' - 2tanx = y'

⇒2y(0)y'(0) - 2tan0 = y'(0)

but y²(0) + 0 = y(0)

y(0) = 0

so, y'(0) = 0

now again differentiating w.r.t x

2y'² + 2yy" - 2sec²x = y"

2y'(0)² + 2y(0)y"(0) - 2sec²0 = y"(0)

⇒y"(0) = 2

Therefore the correct option is (1)