Project ForgeEngineering Mathematics
Differential Equations
GATE 2011
Medium
Which ONE of the following functions y(x) has the slope of its tangent equal to ax/y? (a and b are real constants)
- Ay=(x+b)/a
- By=ax+b
- Cy=√[(x²+b)/a]
- y=√(ax²+b)
Explanation
dy/dx=ax/y ⟹ y dy = ax dx ⟹ y²/2=ax²/2+C ⟹ y²=ax²+2C=ax²+b (renaming the constant) ⟹ y=√(ax²+b).
Source: GATE CH 2011 (2011)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.