Project ForgeEngineering Mathematics
Calculus
GATE 2018
Medium
If y is the solution of the differential equation y³(dy/dx) + x³ = 0, y(0) = 1, the value of y(−1) is
- A−2
- B−1
- 0
- D1
Explanation
Separating variables: y³dy = −x³dx. Integrating: y⁴/4 = −x⁴/4 + C, i.e. y⁴ + x⁴ = 4C. At x=0, y=1: 4C=1, so y⁴ = 1 − x⁴. At x=−1: y⁴ = 1−1 = 0, so y(−1) = 0.
Source: GATE ME 2018 Session 2 (Set 2) (2018)
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