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) = C₁Need Help?√² + 4v² + 1²17 ) y = 011//=/³₁ (0x) + C₂ = = = V₁ (ax)y(x) = C₁₂√xJ₁(ax) + C₂√xy₁ (ax)11O 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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Answered: Use the indicated change of variable to…

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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Show that the following differential equation is an exact equation. (2x+xy -1)dx+(x'y+3)dy = 0, y(1)= 4 Hence, find its particular solution.
Verify that the indicated function y = p(x) is an explicit solution of the given first-order differential equation. 2y = y³ cos(x); y = (1-sin(x))-1/2 When y (1 sin(x))-1/2, = 2y' Thus, in terms of x, y³ cos(x) = Since the left and right hand sides of the differential equation are equal when (1 - sin(x))¯¹ -1/2 is substituted for y, y = (1 - sin(x))-¹/2 is a solution. Proceed as in Example 6, by considering y simply as a function and give its domain. O {x|x * 2nm} # 0 {x|x=+2nx} o{x|x*} 2 O{x|x = 2n} ढ 0{x|x */ +27= } Then by considering p as a solution of the differential equation, give at least one interval I of definition. (27πT, DO) 0 (7,00) π 5x 2 2 [27π, 00) (2,57) O
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The indicated function y, (x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, e-P(x) dx Y2 = Y1(x) | - -dx (5) as instructed, to find a second solution y,(x). x?y" – xy' + 17y = 0; = x sin(4 In(x)) Y2 =
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