O D E

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Problems to workout
1 Solve the IVP y' = x + y + xy, y(0) = 1 by Taylor series expansion for y at x = 0.1 and at x = 0.5

2 Obtain y as a Taylor series of x for the IVP y' = -0.9y/(1+2x), y(0) = 1.

3 Using Taylor series method solve y' = y sin x + cos x, y(0) = 0 at x = 0.5 accurate upto five decimal palces.

4 Solve the IVP xy' = x - y, y(2) = 2 using Taylor series method of order four at x = 2.3