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).
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).
\(2\frac{d^2y}{dx^2}-\frac{dy}{dx}-y=0\)
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).
Updated On: Oct 1, 2024
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