Recent content by utterfly

I simplified the solution to a quadratic equation. It looks OK, except that the constant of integration is attached to 'x' inside the radical. I will make use of it. If you are curious: 'y' is the density, 'x' is the radius of a gas of gravitational waves. The solution relates the density...

f=x^2 y y=f/x^2 dy/dx= -2f/x^3 + (1/x^2)df/dx This seems OK Sorry can't get the sub and sup to work.

The calculation is lengthy. Here goes: f=x^2y (1/x^2)df/dx-2f/x^3=3f/x^3((a+f)/(3-bf)) df/dx=(f/x)((3a+b)+f(3-2b))/(3-bf)) Int((3-bf)/((3a+b)+f(3-2b))df/f=Int(dx/x) (1/(a-2))lnf-(3a/2(3a-6))ln((3a-b)+f(3-2b))=lnx+K The ln terms with f combine into two terms. lnf=2lnx+lny is substituted. When the...

That is true. Taking anti-logs gives the horrible expression I was referring to. But, it is a solution! If you have a simpler expression I would like to see it. Much appreciate your interest and effort.

Hi tiny-tim This is what I get dz/dx=(z/x)((3a+b)+z(3-2b)/(3-bz)) Solving for z gives a bunch of ln terms.

I tried the substitution; I do get a result even if looks horrible! I will repeat the calculation, just to make sure. Thanks guys!

Yes, you can even make it simpler by dividing through by x^2. The terms remaining have both variables. Separation of variables has not been successful. So substitution will not help.

Hi tiny-tim I have tried factoring the equation - but no luck! Can you help with the factoring? Thanks

Hello tiny-tim: It is 3x and not 3ax. I am going to try an iterative approach. Nothing else seems to work. Thanks

Hi Jeffrey The equation is not homogeneous. See if you can find a work around. Thanks

Hello: I discovered this forum while looking for advice on solving a first order nonlinear differential equation. The equation I am trying to solve is dy/dx=(3ay+3bx^2y^2)/(3x-bx^3y) a and b are constants. The equation is not exact, nor is it homogeneous. I have failed to separate the...