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GATE 2020 CH – Question 64

Engineering Mathematics · Differential Equations: First order and higher order equations, Cauchy-Euler equations · 2 marks · Numerical answer

Given dy/dx = y − 20 with y(0) = 40, find y(2), rounded to the nearest integer.

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Correct answer: 162 to 170

Explanation

Set z = y − 20, so z′ = z and z(0) = 20. Thus z(x) = 20eˣ and y(x) = 20 + 20eˣ. At x = 2, y = $20+20e^2=167.7811$, which rounds to 168. This solution also directly satisfies both the ODE and initial value.

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