GATE 2024 MA – Question 44

Ordinary Differential Equations · First Order Equations and Initial Value Problems · 2 marks · Multiple choice

For y′=e^(−y²)+1,y(0)=0, I:the IVP has a unique solution on ℝ. II:Every solution is bounded on its maximal existence interval. Choose truth values.

Both I and II true
I true, II false
I false, II true
Both false

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Show answer and explanation

Correct answer: (B) I true, II false

Explanation

The right side is smooth with bounded derivative, so existence/uniqueness is global; also 1≤y′≤2 prevents finite-time blow-up. For t≥0, y(t)≥t, so the solution is unbounded. **I true, II false, B**.

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