GATE CE 2022 Set 1 — Question 48
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Engineering Mathematics → Numerical Integration & ODEs → Euler Method
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Question
Consider the differential equationFor the initial condition at , the value of at obtained using Euler’s method with a step-size of is _________. (round off to one decimal place)
Correct answer
6.3 to 6.5
Solution
Given the first-order ordinary differential equation:Initial conditions:
Step size:
Target: Find at Euler's iterative formula is given by:Step 1: Calculate at ()
Step 2: Calculate at ()
Thus, the value of at is .
Step size:
Target: Find at Euler's iterative formula is given by:Step 1: Calculate at ()
Step 2: Calculate at ()
Thus, the value of at is .
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