find a D.E with general solution

Find a D.E Y=cx+2c/x
in Algebra 2 Answers by Level 12 User (101k points)

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5 Answers

We can write the given as: y= Ax+B/x
by Level 12 User (101k points)
Then y'=A-B/x^2 & y"=2b/x^3
by Level 12 User (101k points)
Solving the system: A=y'+xy"/2 , B=x^3y"/2
by Level 12 User (101k points)
Substitution in the given: x^2y"+xy'-y=0
by Level 12 User (101k points)
This is an EULER-CAUCHY equation ( homogenous form)
by Level 12 User (101k points)

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