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Solve the initial value problem: y'= x³ +y³ xy² y(x) = 3x³ (logx +9) 2 y(1) = 3 X

Solve the initial value problem: y'= x³ +y³ xy² y(x) = 3x³ (logx +9) 2 y(1) = 3 X

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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Solve the initial value problem: y(x) - y'= 3x³ ( +y³ 2²¹-1²³, y(1) = 3 xy² (logx+9) X Hint: Notice that the equation on the right is homogeneous and see Homework exercise 23 in section 1.2 of our textbook to review techniques for solving homogeneous equations. Note that we've been given an intial value of the form y(a) = b where a > 0, so this only determines a solution corresponding to the right half of the graph of ln(|x|), i.e., the part of the graph corresponding to positive values of x. Therefore, we should write In(x) instead of In(x), since the left half of the
Transcribed Image Text:Solve the initial value problem: y(x) - y'= 3x³ ( +y³ 2²¹-1²³, y(1) = 3 xy² (logx+9) X Hint: Notice that the equation on the right is homogeneous and see Homework exercise 23 in section 1.2 of our textbook to review techniques for solving homogeneous equations. Note that we've been given an intial value of the form y(a) = b where a > 0, so this only determines a solution corresponding to the right half of the graph of ln(|x|), i.e., the part of the graph corresponding to positive values of x. Therefore, we should write In(x) instead of In(x), since the left half of the
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