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Consider a differential equation (dy(x))/(dx)-y(x)=x with the initial condition y(0)=0. Using Euler's first order method with a step size of 0.1, the value of y(0.3) is

1. 0.01
2. 0.031
3. 0.0631
4. 0.1

Correct answer: 0.031

Solution

With y'=y+x, y(0)=0, h=0.1: y(0.1)=0+0.1(0+0)=0; y(0.2)=0+0.1(0+0.1)=0.01; y(0.3)=0.01+0.1(0.01+0.2)=0.031. So y(0.3)=0.031, not 0.0631.

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