|Sep2-08, 07:48 PM||#1|
v substitution in homogeneous equations (diff eq)
Hey all, i think i'm doing most of this right, but i'm missing a coefficient somewhere when integrating or something...
1. The problem statement, all variables and given/known data
Substitute v=y/x into the following differential equation to show that it is homogeneous, and then solve the differential equation.
2. Relevant equations
y=xv(x) => y'=v+xv'
3. The attempt at a solution
divide top and bottom of right hand side by x^2 to get v's and replace y' by v+xv'
subtract v from both sides
put the lonely v on a common denominator
separate v's and x's
the back of the book says the answer is |y^2-x^2|=c|x|^3.
what am i doing wrong? i'm missing a 3 somewhere. i'm kinda rusty with lograthimic algebra, so all help is appreciated. i've gotten a few of these problems wrong by missing a constant or exponent on the right hand of the side of the equation after integrating.
|Sep2-08, 08:09 PM||#2|
These two lines.
Now just simplify again.
|Sep2-08, 11:46 PM||#3|
then i get
which is in the back of the book. thanks!
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