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GATE 2025 MA – Question 35

Numerical Analysis · Numerical Initial Value Problems · 1 mark · Numerical answer

Use Euler with h=0.5 for y′=sin(π(x+y)), y(0)=0. Find approximate y(1.5)+2y(1) (integer).

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Correct answer: 1 to 1

Explanation

First update gives y(0.5)=0 because sin0=0. Next gives y(1)=0+0.5 sin(π/2)=0.5. Third uses x+y=1.5, giving y(1.5)=0.5+0.5 sin(3π/2)=0. Required value=0+2×0.5=**1**.

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