6. {y₁(x) = x, y₂(x) = x²} is a fundamental set of solutions of the reduced equation of x²y" - 2xy + 2y = 4x². The general solution of the equation is: (a) y = C₁+C₂x² + x¹ (b) y = C₁+C₂x² + 4x² ln x (c) y = C₁x + С₂x² + 2x² − x² ln x (d) y = C₁x + С₂x² + x² − 2x³ (e) None of the above.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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6. {y₁(x) = x, y2(x) = x²} is a fundamental set of solutions of the reduced equation of
x²y" - 2xy + 2y = 4x².
The general solution of the equation is:
(a) y = C₁x + C₂x² + x¹
(b) y = C₁x + С₂x² + 4x² ln x
(c) y = C₁x + C₂x² + 2x² - x² ln x
I
(d) y = C₁x + С₂x² + x² - 2x³
(e) None of the above.
Transcribed Image Text:6. {y₁(x) = x, y2(x) = x²} is a fundamental set of solutions of the reduced equation of x²y" - 2xy + 2y = 4x². The general solution of the equation is: (a) y = C₁x + C₂x² + x¹ (b) y = C₁x + С₂x² + 4x² ln x (c) y = C₁x + C₂x² + 2x² - x² ln x I (d) y = C₁x + С₂x² + x² - 2x³ (e) None of the above.
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