Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Ordinary Differential Equations
Consider the following initial value problem (IVP):
\(\frac{dy}{dx} = e^{-x^2 + y}\), \(\quad x \in \mathbb{R}\), y(0) = y0
where (y0) is a real constant. Which of the following option is true?
1
The IVP has a unique solution for every real number (y0).
2
The IVP has exactly two distinct solutions regardless of (y0).
3
The IVP has infinitely many solutions for each (y0).
4
The IVP has no solution for any real number (y0).
5
Question Not Attempted