Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Ordinary Differential Equations Initial Value Problem
Let f : ℝ2 → ℝ be continuous and
f(t, x) < 0 if tx > 0,
f(t, x) > 0 if tx < 0.
Consider the problem of solving the following:
\(\rm \dot{x}\) = f(t, x), x(0) = 0
Which of the following is true?
1
There exists a unique local solution.
2
There exists a local solution but may not be unique.
3
There may not exist any solution.
4
If local solution exists then it is unique.
5
Question Not Attempted