Use Euler's method to obtain numerical solutions on the specified time interval for step sizes h...
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Use Euler's method to obtain numerical solutions on the specified time interval for step sizes h = 0.1, h = 0.05, and h = 0.025. (b) Solve the problem analytically and plot the exact solution and the three numerical solutions on a single graph. Does the error appear to be getting smaller as h is reduced? 7. y' = 2y-1, y(0)=1, 0t 0.5 9. y = y, y(0) = 1, 0t1 8. y'=y+e, y(0) = 0, 0 1 10. y'=-y, y(-1)=2, -1 t0 Use Euler's method to obtain numerical solutions on the specified time interval for step sizes h = 0.1, h = 0.05, and h = 0.025. (b) Solve the problem analytically and plot the exact solution and the three numerical solutions on a single graph. Does the error appear to be getting smaller as h is reduced? 7. y' = 2y-1, y(0)=1, 0t 0.5 9. y = y, y(0) = 1, 0t1 8. y'=y+e, y(0) = 0, 0 1 10. y'=-y, y(-1)=2, -1 t0
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