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Which of the following is the Euler (Cauchy) differential equation whose general solution is y = c,cos(ln(x)) + cz sin(In(x)) ?

Which of the following is the Euler (Cauchy) differential equation whose general solution is y = c,cos(ln(x)) + cz sin(In(x)) ?

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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Which of the following is the Euler (Cauchy) differential equation whose general solution is y = c,cos(In(x)) + c, sin(In(x)) ? a) x2+y = 0 dx² b) x?+ x + 2y = 0 d²y dx² c) x² d²y c) x² - x+ y = 0 dx2 dx d) x² dx? d²y +x +y = 0 dy dx e) x2. dx² d²y +x = 0 dy
Transcribed Image Text:Which of the following is the Euler (Cauchy) differential equation whose general solution is y = c,cos(In(x)) + c, sin(In(x)) ? a) x2+y = 0 dx² b) x?+ x + 2y = 0 d²y dx² c) x² d²y c) x² - x+ y = 0 dx2 dx d) x² dx? d²y +x +y = 0 dy dx e) x2. dx² d²y +x = 0 dy
Expert Solution
Step 1

In this question, the general solution of the Cauchy  equation

y=c1cos(lnx)+c2sin(lnx)

It is two-parameter family so by differentiating it twice, we have

 

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