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Chapter 3: Q 3.6-1E (page 129)

Show that when Euler鈥檚 method is used to approximate the solution of the initial value problem y'=5yy(0) = 1 , at x= 1, then the approximation with step size his(1+5)1h.

Short Answer

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Proved

Step by step solution

01

Apply Euler’s formula

Herey'=5y,y(0)=1

Apply the Euler鈥檚 formula

yn+1=yn+hf(xn,yn)

In our case of differential equation our equation is

yn+1=yn+h5yn

The interval isb-an=1-0n=1n=h

02

Substitute in the Euler’s formula

Now

y1=1(1+5h)y2=1+5h(1+5h)-(1+5h)2...yn=(1+5h)nyn=(1+5h)1h

Hence, it is proved that yn= (1 + 5h)1h

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