Question

For a > 0, let ya(x) be the solution to the differential equation
$2\frac{d^2y}{dx^2}-\frac{dy}{dx}-y=0$
satisfying the conditions
y(0) = 1, y'(0) = a.
Then, the smallest value of a for which ya(x) has no critical points in ℝ equals ___________ (rounded off to the nearest integer).

Answer 1

The correct answer is 1.