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दिखाइए कि फलन y= a cos (logx) + b sin (log x) अवकल समीकरण

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दिखाइए कि फलन y= a cos (logx) + b sin (log x) अवकल समीकरण x2d2y/dx2 + x dy/dx + y = 0 हल है।

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दिया गया फलन

y = a cos (log x) + b sin (log x) …(i)

समीकरण (i) के दोनों पक्षों का x के सापेक्ष अवकलन करने पर, dy a sin (log x) b cos (log x)

समीकरण (ii) का x के सापेक्ष पुनः अवकलन करने पर,

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