Part CCSIR NET December 2023linear-growth-global-existence

Linear growth global existence

Consider the initial value problem y′ = y + ½| $sin (y^{2})$ |, x > 0, y(0) = −1. Which of the following statements are true?

A.There exists an $α \in (0, \infty)$ such that $l i m_{x \to α^{-}}$ |y(x)| $= \infty$ .
B.y(x) exists on $(0, \infty)$ and it is monotone.
C.y(x) exists on $(0, \infty)$ , but not bounded below.
D.y(x) exists on $(0, \infty)$ , but not bounded above.

The answer and working come with the PYQ pack.

The trap it tests

Existence vs uniqueness

A theorem giving one was read as giving both.

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