GATE 2014 EC (EC4) – Question 36
Solve $y^{\prime\prime}+4y^\prime+4y=0$ with $y(0)=y^\prime(0)=1$, and find y(1).
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Show answer and explanation
Correct answer: 0.53 to 0.55
Explanation
The characteristic polynomial is(r+2)², so y=(A+Bx)e⁻²ˣ. Initial value y(0)=1gives A=1. The derivative at0is B−2A=1, so B=3. Therefore y(1)=4e⁻²=**0.541341**.