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x* . y"+x•y'+y=3+sec(In.x), x>0 Show {cos(Inx), sin(In x)} form a fundamental set. #5.) Given а.) b.) Find Ур using Variation of Parameters. Hint: Divide both sides of the differential equation by x- BEFORE you identify f (x). с.) Write the general solution.

x* . y"+x•y'+y=3+sec(In.x), x>0 Show {cos(Inx), sin(In x)} form a fundamental set. #5.) Given а.) b.) Find Ур using Variation of Parameters. Hint: Divide both sides of the differential equation by x- BEFORE you identify f (x). с.) Write the general solution.

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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Subject: US Differential Equation

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#5.) Given \( x^2 \cdot y'' + x \cdot y' + y = 3 + \sec(\ln x) \), \( x > 0 \) a.) Show \(\{ \cos(\ln x), \sin(\ln x) \}\) form a fundamental set. b.) Find \( y_p \) using Variation of Parameters. Hint: Divide both sides of the differential equation by \( x^2 \) BEFORE you identify \( f(x) \). c.) Write the general solution.
Transcribed Image Text:#5.) Given \( x^2 \cdot y'' + x \cdot y' + y = 3 + \sec(\ln x) \), \( x > 0 \) a.) Show \(\{ \cos(\ln x), \sin(\ln x) \}\) form a fundamental set. b.) Find \( y_p \) using Variation of Parameters. Hint: Divide both sides of the differential equation by \( x^2 \) BEFORE you identify \( f(x) \). c.) Write the general solution.
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