Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Ordinary Differential Equations First order Differential Equation
Suppose x : [0, ∞) → [0, ∞) is continuous and x(0) = 0. If (x(t)2 ≤ 2 + \(\int_{0}^{t} \) x(s) ds, ∀t ≥ 0, then which of the following is TRUE?
1
x(√2) ∈ [0, 2]
2
\(\rm x(\sqrt{2}) \in\left[0, \frac{3}{\sqrt{2}}\right]\)
3
\(\rm x(\sqrt{2}) \in\left[\frac{5}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right] \)
4
x(√2)∈[10, ∞)
5
Question Not Attempted