Explanation Given that, the general solution of a homogeneous second-order Cauchy-Euler equation is y = c 1 x 2 + c 2 x 2 ln x , x > 0 . Since this is the solution of the second order Cauchy-Euler differential equation and it have repeated roots, the general solution is given by y = c 1 x m + c 2 x m ln x . The given solution y = c 1 x 2 + c 2 x 2 ln x is the exactly in the form y = c 1 x m + c 2 x m ln x . Hence, the roots are repeated and the roots are m 1 = m 2 = 2 . Thus, the auxiliary equation can be written as mentioned below

Student Solutions Manual For Zill's A First Course In Differential Equations With Modeling Applications, 11th

11th Edition

ISBN: 9781305965737

Author: Dennis G. Zill

Publisher: Brooks Cole

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Chapter 4, Problem 7RE

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To-fill: The blank in the statement “If y=c1x2+c2x2lnx,x>0, is a general solution of a homogeneous second-order Cauchy-Euler equation, then the DE is ______.”

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Chapter 4, Problem 6RE

Chapter 4, Problem 8RE

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Chapter 4 Solutions

Student Solutions Manual For Zill's A First Course In Differential Equations With Modeling Applications, 11th

Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - Given that y=c1+c2x2 is a two-parameter family of...Ch. 4.1 - Find two members of the family of solutions in...Ch. 4.1 - Given that x(t) = c1 cos t + c2 sin t is the...Ch. 4.1 - Use the general solution of x + 2x = 0 given in...Ch. 4.1 - In Problems 9 and 10 find an interval centered...Ch. 4.1 - In Problems 9 and 10 find an interval centered...

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To-fill: The blank in the statement “If y = c 1 x 2 + c 2 x 2 ln x , x > 0 , is a general solution of a homogeneous second-order Cauchy-Euler equation, then the DE is _ _ _ _ _ _ .”

Solution Summary: The author explains that the general solution of a homogeneous second-order Cauchy-Euler equation is y=c_1x2+

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To-fill: The blank in the statement “If y=c1x2+c2x2lnx,x>0, is a general solution of a homogeneous second-order Cauchy-Euler equation, then the DE is ______.”

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Chapter 4 Solutions

To-fill: The blank in the statement “If y = c 1 x 2 + c 2 x 2 ln x , x &gt; 0 , is a general solution of a homogeneous second-order Cauchy-Euler equation, then the DE is _ _ _ _ _ _ .”

Solution Summary: The author explains that the general solution of a homogeneous second-order Cauchy-Euler equation is y=c_1x2+

Videos

To-fill: The blank in the statement “If y=c1x2+c2x2lnx,x>0, is a general solution of a homogeneous second-order Cauchy-Euler equation, then the DE is ______.”

Want to see the full answer?

Chapter 4 Solutions

To-fill: The blank in the statement “If y = c 1 x 2 + c 2 x 2 ln x , x > 0 , is a general solution of a homogeneous second-order Cauchy-Euler equation, then the DE is _ _ _ _ _ _ .”