In the Euler method for y'=1+y/x, y(1)=2, h=0.25, after step 1 we have y_1approx2.75. The function value f(x_1,y_1)=f(1.25, 2.75) equals:

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SSC Applied Mathematics QUESTION #1330

Question 1

In the Euler method for \(y'=1+y/x\), \(y(1)=2\), \(h=0.25\), after step 1 we have \(y_1\approx2.75\). The function value \(f(x_1,y_1)=f(1.25, 2.75)\) equals:

\(3.2\)✔️
\(2.5\)
\(3.0\)
\(3.5\)

Correct Answer Explanation

\(f(1.25,2.75)=1+\dfrac{2.75}{1.25}=1+2.2=3.2\). This is used in the next Euler step: \(y_2=2.75+0.25\times3.2=2.75+0.80=3.55\).

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