- #1
Michels10
- 18
- 0
Solve y' = y/x + 1/y
I get a similar answer to the correct one but I believe I am making a substitution error. Here is my attempt:
dy/dx = y/x + 1/y
set v = y/x
equation now becomes: v + x(dv/dx) = v + 1/(x*v)
reduces to: dv/dx = 1/(x^2 * v)
Now the equation is seperable, so I separate and take the integral of both sides yielding:
v = (sqrt(-2) * sqrt(x*c - 1))/sqrt(x)
--even if i substitute v = y/x back in it doesn't come out to be the correct solution of:
y = sqrt(x) * sqrt(x*c -2)
Any insight would be great!
I get a similar answer to the correct one but I believe I am making a substitution error. Here is my attempt:
dy/dx = y/x + 1/y
set v = y/x
equation now becomes: v + x(dv/dx) = v + 1/(x*v)
reduces to: dv/dx = 1/(x^2 * v)
Now the equation is seperable, so I separate and take the integral of both sides yielding:
v = (sqrt(-2) * sqrt(x*c - 1))/sqrt(x)
--even if i substitute v = y/x back in it doesn't come out to be the correct solution of:
y = sqrt(x) * sqrt(x*c -2)
Any insight would be great!