GATE 2018 ME (ME2) – Question 46
Solve $y^{\prime\prime}+y^\prime-6y=0$ with $y(0)=0$, $y^\prime(0)=1$. Find y(1), to two decimal places.
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Show answer and explanation
Correct answer: 1.45 to 1.48
Explanation
The characteristic equation $r^2+r-6=0$ has roots 2 and −3. Thus $y=Ae^{2x}+Be^{-3x}$. Conditions give $A+B=0$ and $2A-3B=1$, so $A=1/5$, $B=-1/5$. Therefore $y(1)=(e^2-e^{-3})/5=1.467854$: **1.47**.