Project ForgeEngineering Mathematics
Calculus
GATE 2011
Medium
Consider the differential equation dy/dx = (1+y²)x. The general solution with constant c is
- Ay = tan(x²/2) + tan c
- By = tan²(x/2 + c)
- Cy = tan²(x/2) + c
- y = tan(x²/2 + c)
Explanation
Separating variables: dy/(1+y²) = x dx. Integrating both sides: tan⁻¹(y) = x²/2 + c, so y = tan(x²/2 + c).
Source: GATE ME 2011 (2011)
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