Project ForgeEngineering Mathematics
Differential Equations
GATE 2013
Medium
The solution of the differential equation dy/dx−y²=0, given y=1 at x=0, is
- A1/(1+x)
- 1/(1−x)
- C1/(1−x)²
- Dx³/3 + 1
Explanation
Separating: dy/y²=dx ⟹ −1/y=x+C. At x=0,y=1: −1=C. So −1/y=x−1 ⟹ 1/y=1−x ⟹ y=1/(1−x).
Source: GATE CH 2013 (2013)
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