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Use the indicated change of variable to find the general solution of the given differential equation on (0, ∞). (The definitions of various Bessel functions are given here.) x²y" + (a²x² = √² + ¹² ) y = 0; O y(x) = C₁(x) + C₂₁(x) O y(x) = C₁ √xJ, (ax) + C₂√xY₁(x) = C₁₂/³₁ (ax) + C₂ √²_₁(ax) Oy(x) = C₂ = 0; y = √xv(x) O y(x) = C₁ √xJ₁ (ax) + C₂√x³_₁(ax) O y(x) = C₁₂(ax) + C₂Y₁(ax) Need Help? Submit Answer Read It

Use the indicated change of variable to find the general solution of the given differential equation on (0, ∞). (The definitions of various Bessel functions are given here.) x²y" + (a²x² = √² + ¹² ) y = 0; O y(x) = C₁(x) + C₂₁(x) O y(x) = C₁ √xJ, (ax) + C₂√xY₁(x) = C₁₂/³₁ (ax) + C₂ √²_₁(ax) Oy(x) = C₂ = 0; y = √xv(x) O y(x) = C₁ √xJ₁ (ax) + C₂√x³_₁(ax) O y(x) = C₁₂(ax) + C₂Y₁(ax) Need Help? Submit Answer Read It

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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Use the indicated change of variable to find the general solution of the given differential equation on (0, ∞). (The definitions of various Bessel functions are given here.) x²y" + y² + (a²x² - - . O y(x) = C₁ Need Help? √² + 4 v² + 1²17 ) y = 0 1 1 //=/³₁ (0x) + C₂ = = = V₁ (ax) y(x) = C₁₂√xJ₁(ax) + C₂√xy₁ (ax) 1 1 O y(x) = C₁₂(x) + ₂√(x) Submit Answer = 0; y = √xv(x) O y(x) = C₁ √xJ₁(ax) + C₂√x³_₁(ax) O y(x) = C₁J₁(xx) + C₂Y(ax) Read It
Transcribed Image Text:Use the indicated change of variable to find the general solution of the given differential equation on (0, ∞). (The definitions of various Bessel functions are given here.) x²y" + y² + (a²x² - - . O y(x) = C₁ Need Help? √² + 4 v² + 1²17 ) y = 0 1 1 //=/³₁ (0x) + C₂ = = = V₁ (ax) y(x) = C₁₂√xJ₁(ax) + C₂√xy₁ (ax) 1 1 O y(x) = C₁₂(x) + ₂√(x) Submit Answer = 0; y = √xv(x) O y(x) = C₁ √xJ₁(ax) + C₂√x³_₁(ax) O y(x) = C₁J₁(xx) + C₂Y(ax) Read It
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