Question

If y² + log_e (cos² x) = y, x ∈ ( -π/2, π/2) then : 

(1) |y"(0)| = 2 

(2) |y'(0)| + |y"(0)| = 3 

(3) |y'(0)| + |y"(0)| = 1 

(4) y"(0) = 0

Answer 1

(1) |y"(0)| = 2 

Differentiating wrt x 

Þ 2yy' – 2 tan x = y' 

At (0, 0) y' = 0 

At (0, 1) y' = 0 

Differentiating wrt x 

2yy" + 2(y') 2 – 2 sec 2 x = y" 

At (0, 0) y" = –2 

At (0, 1) y" = 2 

\(\therefore\) |y"(0)| = 2