(35 points) Problem 2: Use the Euler's and classical RK-4 methods to solve the following differential...

Transcribed Image Text:

(35 points) Problem 2: Use the Euler's and classical RK-4 methods to solve the following differential equation: 3xy"-xx+y=0; x(1) = 4, y'(1) = 2 On the interval [1,2] with h = 0.2. (A) [10 points] Solve it to get a true solution using the following substitution method: y = xx (B) [5 points] Cast this DE into an autonomous system of first order differential equations using y1, y2, etc. Provide the IVPS in that form as well. (C)[10 points] Fill out the following table for Euler's method. Show your work for full credit. X Y1 Y2 Exact 1.0 4.00 2.00 4.00 1.2 1.4 1.6 (D)[10 points] Fill out the initial step for the RK-4 method. Show your work for full credit. X K11 K12 K21 K22 K31 K32 K41 K42 Y1 1.0 Y2 4.00 2.00 1.2 (35 points) Problem 2: Use the Euler's and classical RK-4 methods to solve the following differential equation: 3xy"-xx+y=0; x(1) = 4, y'(1) = 2 On the interval [1,2] with h = 0.2. (A) [10 points] Solve it to get a true solution using the following substitution method: y = xx (B) [5 points] Cast this DE into an autonomous system of first order differential equations using y1, y2, etc. Provide the IVPS in that form as well. (C)[10 points] Fill out the following table for Euler's method. Show your work for full credit. X Y1 Y2 Exact 1.0 4.00 2.00 4.00 1.2 1.4 1.6 (D)[10 points] Fill out the initial step for the RK-4 method. Show your work for full credit. X K11 K12 K21 K22 K31 K32 K41 K42 Y1 1.0 Y2 4.00 2.00 1.2