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GATE 2026 BT – Question 58

Engineering Mathematics · Differential Equations: First order ODEs, higher order ODEs with constant coefficients, Cauchy and Euler equations, Laplace transforms · 2 marks · Numerical answer

From the following plot of $\frac{dy}{dx}$ versus $x$ and if y(2) = 5, the value of y(3) is ________. (rounded off to one decimal place)

A plot of $\frac{dy}{dx}$ against $x$ for $x$ from 0 to 3. It is a straight line through the points (0, 1), (1, 2), (2, 3) and (3, 4).

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Correct answer: 8.46 to 8.54

Explanation

The line is $\frac{dy}{dx} = x + 1$. So $y(3) - y(2) = \int_2^3(x + 1)dx = \left[\frac{x^2}{2} + x\right]_2^3 = 7.5 - 4 = 3.5$, and $y(3) = 5 + 3.5 = 8.5$.