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a. Show that the particular solution is y = 3x2 (In xº + x³ + 2). b. Use the 2nd, grd and 4th Runge-Kutta methods to approximate the value of y at x = 2 using a step size of h = 0.1. Complete the table below. RK Method Step size Approx. value of y Abs. Err. Rel. Abs. Err. (%) RK-2 0.1 RK-3 0.1 RK-4 0.1 Show details of computation below (or paste a screenshot of Excel computation).

a. Show that the particular solution is y = 3x2 (In xº + x³ + 2). b. Use the 2nd, grd and 4th Runge-Kutta methods to approximate the value of y at x = 2 using a step size of h = 0.1. Complete the table below. RK Method Step size Approx. value of y Abs. Err. Rel. Abs. Err. (%) RK-2 0.1 RK-3 0.1 RK-4 0.1 Show details of computation below (or paste a screenshot of Excel computation).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. Consider the ODE 2 y' + -y = +1 x3 With the initial condition that y=1 when x = 1. 1 Show that the particular solution is y = (In x° + x³ + 2). а. 3x2 b. Use the 2nd, grd and 4th Runge-Kutta methods to approximate the value of y at x = 2 using a step size of h = 0.1. Complete the table below. RK Method Step size Approx. value of y Abs. Err. Rel. Abs. Err. (%) RK-2 0.1 RK-S 0.1 RK-4 0.1 Show details of computation below (or paste a screenshot of Excel computation).
Transcribed Image Text:2. Consider the ODE 2 y' + -y = +1 x3 With the initial condition that y=1 when x = 1. 1 Show that the particular solution is y = (In x° + x³ + 2). а. 3x2 b. Use the 2nd, grd and 4th Runge-Kutta methods to approximate the value of y at x = 2 using a step size of h = 0.1. Complete the table below. RK Method Step size Approx. value of y Abs. Err. Rel. Abs. Err. (%) RK-2 0.1 RK-S 0.1 RK-4 0.1 Show details of computation below (or paste a screenshot of Excel computation).
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