Question:medium

Consider the differential equation \[ \frac{dy}{dx}=x^{2}-y,\qquad y(0)=1. \] Using the Simple Euler's Method with a step size of \(h=0.1\), the value of \(y(0.1)\) is

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Remember the Simple Euler's Method formula: \[ \boxed{ y_{n+1}=y_n+h\,f(x_n,y_n) } \] To solve numerical problems quickly:
• Identify \(x_0,\;y_0,\) and the step size \(h\).
• Compute the slope \(f(x_0,y_0)\).
• Substitute directly into Euler's formula.
• Each application of the formula advances the solution by one step of length \(h\). This is one of the most frequently asked numerical methods in engineering mathematics examinations.

Updated On: Jul 4, 2026

\(0.1\)
\(0.7\)
\(0.9\)
\(1.0\)

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The Correct Option is C

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