Help me solve some differential equations

[comnint]

differential equations

please help me for solve this differential equation

equation is in attach file[/img]

 

[ihab]

Re: differential equations

i tried doing my best still dont no how it may be solved????

 

[heo83]

differential equations

Me, too.
At first, I thought this is just an ordinary diff equation, just like:
y' = y + x
But it's really a big problem when y' is in the denominator like this
1/y' = 1/y + 1/x
This diff equation does not have the form like any that I've learnt before. Maybe it's just because I don't know how to use sub-variable.
However, I think there are some diff equations having root that can not be expressed by normal functions that we've known.
Does anyone here know how to prove the root of this diff equation can not be expressed by normal functions like sin, cos, exponential, polynomical,...?

 

[nand_gates]

Re: differential equations

I am also very much interested in solution of this differntial equation.
I also tried hard enough but no luck. It seems to be a nonlinear differntial
eq.

-nand_gates

 

[dazhen]

differential equations

I will suggest you to try Fourier transform. It may helps on the difficulty of 1/y'.

 

[nand_gates]

Re: differential equations

From where you got this differential eq. that may also help to solve it!

 

[gitarrelieber]

Re: differential equations

Differential equation whose solution satifies the existence and uniqueness can be solved by using Lie-algebra. The problem then is to find the suitable infinitesimal transformation which can be admitted by the equation itself. More information in the classic book "Symmetries and Differential Equations" G.W.Bluman, S.Kumei, Springer-Verlag 1989. A powerful package for Mathematica developed by Gerd Baumann is availabe in his book "Symmetry Analysis of Differential Equation with Mathematica".

 

[snaider]

Re: differential equations

you can always try to transform the differential equations , win fourier or laplace , quite always is the best way

 

[DrDolittle]

Re: differential equations

Please write the following in a sheet of paper for better understanding of the expressions




dy/dx = (x*y)/(x+y)

y' = dy/dx

so, (x*y')+(y*y') = (x*y)

y + (x*y')+(y*y') = y + (x*y)

d(xy)/dx + .5 d(y^2)/dx = y(1+x)

i/yd(xy) + [ (.5/y) d(y^2)] = (1+x)dx

I dont know what to do after this,perhaps this may be much use

Regards
drdolittle