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(6) (a) Solve the initial value problem z²y + 2xy = 6r", y(1) = 0. (i) First, differentiate (r²y) with product rule. (ii) Second, match the outcome of the previous step with the equation. (iii) Apply Fundamental Theorem of Calculus to recover y(r), up to a constant. (iv) Match the initial condition given to find the unique solution. (b) Use direction field to verify the solution you got is correct. Show the direction field plot.

(6) (a) Solve the initial value problem z²y + 2xy = 6r", y(1) = 0. (i) First, differentiate (r²y) with product rule. (ii) Second, match the outcome of the previous step with the equation. (iii) Apply Fundamental Theorem of Calculus to recover y(r), up to a constant. (iv) Match the initial condition given to find the unique solution. (b) Use direction field to verify the solution you got is correct. Show the direction field plot.

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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(6) (a) Solve the initial value problem z²y + 2xy = 6r", y(1) = 0. (i) First, differentiate (r²y) with product rule. (ii) Second, match the outcome of the previous step with the equation. (iii) Apply Fundamental Theorem of Calculus to recover y(r), up to a constant. (iv) Match the initial condition given to find the unique solution. (b) Use direction field to verify the solution you got is correct. Show the direction field plot. (7) (a) Solve the initial value problem z²y + 2ry=6r", y(1) = 1. (b) Use direction field to verify the solution you got is correct. Show the direction field plot.
Transcribed Image Text:(6) (a) Solve the initial value problem z²y + 2xy = 6r", y(1) = 0. (i) First, differentiate (r²y) with product rule. (ii) Second, match the outcome of the previous step with the equation. (iii) Apply Fundamental Theorem of Calculus to recover y(r), up to a constant. (iv) Match the initial condition given to find the unique solution. (b) Use direction field to verify the solution you got is correct. Show the direction field plot. (7) (a) Solve the initial value problem z²y + 2ry=6r", y(1) = 1. (b) Use direction field to verify the solution you got is correct. Show the direction field plot.
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