GATE 2024 IN – Question 34
A system satisfies $dy/dt=y+2t-t^2$, with $y(0)=1$ and $0\le t<\infty$. Using improved Euler with step size $h=0.1$, the value of $y(0.1)$ is ______ (two decimal places).
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Correct answer: 1.10 to 1.12
Explanation
Initial slope is $f(0,1)=1$. Euler predictor: $y_p=1+0.1(1)=1.1$. Endpoint slope: $f(0.1,1.1)=1.1+0.2-0.01=1.29$. Improved Euler averages these slopes: $y(0.1)\approx1+0.1(1+1.29)/2=1.1145$. Rounded answer: **1.11**.