Project ForgeEngineering Mathematics
Calculus
GATE 2007
Medium
The solution of dy/dx = y² with initial value y(0)=1 is bounded in the interval
- A−∞ ≤ x ≤ ∞
- −∞ ≤ x ≤ 1
- Cx<1, x>1
- D−2 ≤ x ≤ 2
Explanation
Separating and integrating: −1/y=x+C; y(0)=1 gives C=−1, so y=1/(1−x). This solution is finite and well-defined for all x<1, blowing up at x=1, so it remains bounded on (−∞,1).
Source: GATE ME 2007 (2007)
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