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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.) = 0; y = √√√xv(x) " + (a²x² - 1 ² - √² + 1/1 ) y = 0 x²y" + ○ y(x) = C₁√ √ √(ax) + C₂-, (ax) ○ y(x) = C₁√√x]₁(ax) + C₂√√xy(ax) ● y(x) = C₁₁(αx) + C₂Y₁₂(ax) ○ y(x) = C₁√√√׳₁(αx) + C₁₂√√x]_(ax) = C₁√ √ √(ax) + C₁₂+x₁ (ax) ○ y(x) = C₁

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.) = 0; y = √√√xv(x) " + (a²x² - 1 ² - √² + 1/1 ) y = 0 x²y" + ○ y(x) = C₁√ √ √(ax) + C₂-, (ax) ○ y(x) = C₁√√x]₁(ax) + C₂√√xy(ax) ● y(x) = C₁₁(αx) + C₂Y₁₂(ax) ○ y(x) = C₁√√√׳₁(αx) + C₁₂√√x]_(ax) = C₁√ √ √(ax) + C₁₂+x₁ (ax) ○ y(x) = C₁

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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.) = 0; y = √√√xv(x) " + (a²x² - 1 ² - √² + 1/1 ) y = 0 x²y" + ○ y(x) = C₁√ √ √(ax) + C₂-, (ax) ○ y(x) = C₁√√x]₁(ax) + C₂√√xy(ax) ● y(x) = C₁₁(αx) + C₂Y₁₂(ax) ○ y(x) = C₁√√√׳₁(αx) + C₁₂√√x]_(ax) = C₁√ √ √(ax) + C₁₂+x₁ (ax) ○ y(x) = C₁
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.) = 0; y = √√√xv(x) " + (a²x² - 1 ² - √² + 1/1 ) y = 0 x²y" + ○ y(x) = C₁√ √ √(ax) + C₂-, (ax) ○ y(x) = C₁√√x]₁(ax) + C₂√√xy(ax) ● y(x) = C₁₁(αx) + C₂Y₁₂(ax) ○ y(x) = C₁√√√׳₁(αx) + C₁₂√√x]_(ax) = C₁√ √ √(ax) + C₁₂+x₁ (ax) ○ y(x) = C₁
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