y(2.5) = 15.9389 is Use euler's method with step size 0.1 to estimate y(2.5), where y(x) is the solution of the initial-value problem.
What is euler's method?
First-order methods, such as the Euler method, have local errors that are proportional to the square of the step size and global errors that are proportional to the step size.
f(x,y) = 3y+2xy
So, starting at t0 = 2, repeat the above sequence until t0>2.5
a) m = f(2,1) = 3(1)+2(2)(1) = 7
b) y1 = y0 + hm = 1+0.1(7) = 1.7
c) t1 = t0 + h = 2.1
d) show t1 and y1
e) t0 = t1 = 2.1
f) y0 = y1 = 1.7
2nd iteration
a) m = f(2.1,1.7) = 3(1.7)+2(2.1)(1.7) = 5.1 + 7.14 = 12.24
b) y1 = y0 + hm = 1.7+0.1(12.24) = 1.7 + 1.224 = 2.924
c) t1 = t0 + h = 2.2
d) show t1 and y1
e) t0 = t1 = 2.2
f) y0 = y1 = 2.924
This is what I got for all iterations from a simple program x y
2.1 1.7
2.2 2.924
2.3 5.08776
2.4 8.9544576
2.5 15.938934528
y(2.5) = 15.9389
Learn more about Euler method
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