Project ForgeEngineering Mathematics
Calculus
GATE 2008
Medium
It is given that y″+2y′+y=0, y(0)=0, y(1)=0. What is y(0.5)?
- 0
- B0.37
- C0.62
- D1.13
Explanation
The characteristic equation has a repeated root -1, so y=(A+Bt)e^(-t). y(0)=A=0. y(1)=B·1·e^(-1)=0 ⟹ B=0 (since e^(-1)≠0). So y≡0 everywhere, including y(0.5)=0.
Source: GATE ME 2008 (2008)
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.