Project ForgeEngineering Mathematics
Numerical Methods
GATE 2014
Medium
Consider the differential equation dy/dx = x + ln(y); y=2 at x=0. The solution of this equation at x=0.4 using Euler method with a step size of h=0.2 is
2.35(± 0.05 accepted)
Explanation
Step 1 (x=0→0.2): y'=0+ln(2)=0.6931. y(0.2)=2+0.2×0.6931=2.1386. Step 2 (x=0.2→0.4): y'=0.2+ln(2.1386)=0.2+0.7602=0.9602. y(0.4)=2.1386+0.2×0.9602=2.331.
Source: GATE CH 2014 (2014)
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