Teaching CSIR NET Mock Test Series Mathematical Science Ordinary Differential Equations Initial Value Problem
Consider the initial value problem (IVP)
\(\rm \left\{\begin{matrix}y'(x)=\sqrt{|y(x)+ε|}, & x ∈ R\\\ y(0)=y_0\end{matrix}\right.\)
Consider the following statements:
S1: There is an ε > 0 such that for all y0 ∈ ℝ, the IVP has more than one solution.
S2: There is a \(y_0 \in \mathbb{R}\) such that for all ε > 0, the IVP has more than one solution.
Then
1
both S1 and S2 are true
2
S1 is true but S2 is false
3
S1 is false but S2 is true
4
both S1 and S2 are false