Teaching DSSSB TGT Mock Test 2025 Mathematical Science Ordinary Differential Equations Initial Value Problem
Let f ∶ ℝ2 → ℝ be a locally Lipschitz function. Consider the initial value problem
ẋ = f(t, x), x(t0) = x0
for (t0, x0) ∈ ℝ2. Suppose that J(t0, x0) represents the maximal interval of existence for the initial value problem. Which of the following statements is true?
1
J(t0, x0) = ℝ.
2
J(t0, x0) is an open set.
3
J(t0, x0) is a closed set.
4
J(t0, x0) could be an empty set.