- Consider The Following Initial Value Problem Answer Parts A Through C Below Dy 7xx Y 0 Y 1 2 P X Simplify Yo 1 (25.45 KiB) Viewed 12 times
- Consider The Following Initial Value Problem Answer Parts A Through C Below Dy 7xx Y 0 Y 1 2 P X Simplify Yo 2 (39.39 KiB) Viewed 12 times
- Consider The Following Initial Value Problem Answer Parts A Through C Below Dy 7xx Y 0 Y 1 2 P X Simplify Yo 3 (25.45 KiB) Viewed 12 times
- Consider The Following Initial Value Problem Answer Parts A Through C Below Dy 7xx Y 0 Y 1 2 P X Simplify Yo 4 (25.45 KiB) Viewed 12 times
- Consider The Following Initial Value Problem Answer Parts A Through C Below Dy 7xx Y 0 Y 1 2 P X Simplify Yo 5 (25.45 KiB) Viewed 12 times
- Consider The Following Initial Value Problem Answer Parts A Through C Below Dy 7xx Y 0 Y 1 2 P X Simplify Yo 6 (37.77 KiB) Viewed 12 times
(b) Apply Euler's method with step size h0.15 to approximate this solution on the interval -1xx0.5. Note that, from these data alone, you might not suspect any difficulty near x=0. The reason is that the numerical approximation Jumps across the discontinulty to another solution of 5xy+y=0 for x>0. (Do not round until the final answer. Then round to four decimal places as needed.) Euler Approximation, h=0.15 X -1.00 -0.85 -0.70 -0.55 -0.40 -0.25 -0.10 0.05 0.20 0.35 0.50 (c) Finally apply Euler's method with step stres h 0.03 and h-0.006, but stil prinding results only at the original points, x-1.00 -0.85, -0.700.20.0.35, and 0.50 (Do not round until the final answer. Then round to four decimal places as needed) -1.00 -0.85-0.70 -0.55 -0.40 -0.25 -0.10 0.00 0.20 0.35 0.50 ㅁㅁㅁㅁㅁㅁㅁ Euler Approximation 000 h=0.000 Would you now suspect a discontinuity in the exact solution? Select the correct choice below and, if necessary, fil in the answer box to complete your choice. Euler Approximation OA Yes; before the Euler approximations of y are relatively equal to one another for each value of h. After this value of the Euler approximations are significantly different from each other for each value of h (Type an integer or a decimal) OB No the Euer approximations continue to increase at a relatively consistent rate after the gap that contains the known discontinuity. So, it would be unreasonable to conclude there is a discontinuity based on these data alone. OC. Yes; after x=, the Euler approximations of y are relatively equal to one another for each value of h. Before this value of x, the Euler approximations are significantly different from each other for each value of h (Type an Integer or a decimal) OD. No, the Euler approximations continue to decrease at a relatively consistent rate after the gap that contains the known discontinuity. So, it would be unmasonable to conclude there is a discontinuity based on
Consider the following initial value problem. Answer parts (a) through (c) below. dy 7xx+y=0, y(-1)=2 p(x)= (Simplify your answer.) Use p(x) and integration to find the general solution of the differential equation. 3 y(x) = Apply the initial condition to find the appropriate particular solution. 2 y(x)= (b) Apply Euler's method with step size h= 0.15 to approximate this solution on the interval -1 ≤x≤0.5. Note that, from these data alone, you might not suspect any difficulty near x = 0. The reason is that the numerical approximation "jumps across the discontinuity" to another solution of 7xy + y = 0 for x > 0. (Do not round until the final answer. Then round to four decimal places as needed.) Euler Approximation, h=0.15 X -1.00
(b) Apply Euler's method with step size h0.15 to approximate this solution on the interval -1x*0.5. Note that, from these data alone, you might not suspect any difficulty near x = D. The reason is that the numerical approximation Jumps across the discontinulty" to another solution of 5xy' y=0 for x>0. (Do not round until the final answer. Then round to four decimal places as needed.) X -1.00 -0.85 -0.70 -0.55 -0.40 -0.25 -0.10 0.05 0.20 0.35 0.50 Euler Approximation, h=0.15 (e) Finally apply Euler's method with step sizes h 0.03 and h-0.006, but still printing results only at the original points, x-1.00 -0.85 -0.700.20, 0.35, and 0.50 (Do not round until the final answer. Then round to four decimal places as needed) -1.00 -0.85 Euler Approximation -0.55 -0.40 -0.25 -0.10 0.00 0.20 0.35 0.50 ㅁㅁㅁㅁㅁㅁ 000 Euler Approximation 0 000 h=0.006 Would you now suspect a discontinuity in the exact solution? Select the correct choice below and, if necessary, fill in the snewer box to complete your choice OA Yes; before x the Euler approximations of y are relatively equal to one another for each value of h. After this value of the Euler approximations are significantly different from each other for each value of h (Type an integer or a decimal) OB No: the Euer approximations continue to increase at a relatively consistent rate after the gap that contains the known discontinuity. So, it would be unreasonable to conclude there is a discontinuity based on these data alone. OC. Yes; afterx the Euler approximations of y are relatively equal to one another for each value of h. Before this value of x, the Euler approximations are significantly different from each other for each value of h (Type an Integer or a decimal) OD No: the Euer approximations continue to decrease at a relatively consistent rate after the gap that contains the known discontinuity. So, it would be unreasonable to conclude there is a discontinuity based on