Question

Solve the initial value problem yy' = x, y(0) = 1, using the Euler method in 0 < x< 0.8, with h = 0.2 and h = 0.1, compare results with exact solution at x = 0.8

Answer 1

Answer:

²x²-3abx+2b²=0

or, {(ax)²-2.ax.3b/2+(3b/2)²}+2b²-9b²/4=0

or, (ax-3b/2)²+(8b²-9b²)/4=0

or, (ax-3b/2)²-(b/2)²=0

or, (ax-3b/2+b/2)(ax-3b/2-b/2)=0

or, (ax-b)(ax-2b)=0

Either, ax-b=0

or, ax=b

or, x=b/a

Or, ax-2b=0

or, ax=2b

or, x=2b/a

∴, the roots of the given equations are: b/a, 2b/a. Ans.

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