Teaching CSIR NET Mock Test Series Mathematical Science Ordinary Differential Equations Initial Value Problem
Consider the following initial value problem
\(y^{\prime}=y+\frac{1}{2}|\sin \left(y^2)\right|,\), x > 0, y(0) = -1
Which of the following statements are true?
1
there exists an α ∈ (0, ∞) such that \(\displaystyle\lim _{x \rightarrow \alpha^{-}}|y(x)|=\infty\)
2
y(x) exists on (0, ∞) and it is monotone
3
y(x) exists on (0, ∞), but not bounded below
4
y(x) exists on (0, ∞), but not bounded above