GATE 2022 CE (CE1) – Question 48
For $dy/dx=4(x+2)-y$, with $y(1)=3$, find y(1.4) by Euler’s method with step 0.2 (one decimal).
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Correct answer: 6.37 to 6.43
Explanation
Use $y_{n+1}=y_n+h[4(x_n+2)-y_n]$ with h=0.2. From (1,3), the first slope is $4(3)-3=9$, giving $y(1.2)=4.8$.
The next slope is $4(3.2)-4.8=8$, giving $y(1.4)=4.8+0.2(8)=\mathbf{6.4}$.