Find the general solution of the following differential equations. (1) y"+2y+y=xe¯* [Hint: the basic rule is to guess yp = (Ax + B)e¯x, but you need to multiply by m x™ until every term is not the same as the homogeneous solution] (2) x²y"-2xy'+2y = xlnx (Method1: undetermined coefficient, By change of variable, let t=lnx or x=et, you turn the D.E. into constant coefficient such that you can find a yp by the method of undetermined coefficient) (3) x²y"-2xy'+2y = xlnx (Method 2: Variation of parameters)
Find the general solution of the following differential equations. (1) y"+2y+y=xe¯* [Hint: the basic rule is to guess yp = (Ax + B)e¯x, but you need to multiply by m x™ until every term is not the same as the homogeneous solution] (2) x²y"-2xy'+2y = xlnx (Method1: undetermined coefficient, By change of variable, let t=lnx or x=et, you turn the D.E. into constant coefficient such that you can find a yp by the method of undetermined coefficient) (3) x²y"-2xy'+2y = xlnx (Method 2: Variation of parameters)
ChapterB: Graphical Analysis Of Planar Trusses
Section: Chapter Questions
Problem 3P
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![Find the general solution of the following differential equations.
(1) y"+2y+y=xe¯*
[Hint: the basic rule is to guess yp = (Ax + B)e¯x, but you need to multiply by
m
x™ until every term is not the same as the homogeneous solution]
(2) x²y"-2xy'+2y = xlnx (Method1: undetermined coefficient, By change of
variable, let t=lnx or x=et, you turn the D.E. into constant coefficient such that you
can find a yp by the method of undetermined coefficient)
(3) x²y"-2xy'+2y = xlnx (Method 2: Variation of parameters)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16c9709a-f291-4ea4-acf6-02d313e8dba5%2F1f896efe-d63a-4cf9-9a0c-c2b4eca0e07b%2Flcowqqf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find the general solution of the following differential equations.
(1) y"+2y+y=xe¯*
[Hint: the basic rule is to guess yp = (Ax + B)e¯x, but you need to multiply by
m
x™ until every term is not the same as the homogeneous solution]
(2) x²y"-2xy'+2y = xlnx (Method1: undetermined coefficient, By change of
variable, let t=lnx or x=et, you turn the D.E. into constant coefficient such that you
can find a yp by the method of undetermined coefficient)
(3) x²y"-2xy'+2y = xlnx (Method 2: Variation of parameters)
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