Intro. to Differential Equations

[Astronuc]

I had to solve a first-order nonlinear ODE which led me to a this equation.how can I find the solution for y?
ye^y=f(x)

Where are the derivatives, e.g., y', or differentials?

 

[HallsofIvy]

I had to solve a first-order nonlinear ODE which led me to a this equation.how can I find the solution for y?
ye^y=f(x)

"Lambert's W function", W(x), is defined as the inverse function to f(x)= xe^x. Taking the W function of both sides gives y= W(f(x)).

 

[Erfan]

So the question should be solved numerically using the Lambert's W function? I mean that can't we then have a function in the form: y=f(x)? or we can no more go further than the Lambert's W function?

 

[chwala]

Sounds great! Tutorials like this have been very successful here.

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Mathematicians,
i need an insight and understanding of asymptotic behaviour as applied to singular cauchy problem...anyone can comment...
ken chwala BSC MATHS, MSC APPLIED MATHS FINALIST

 

[benz31345]

good job

 

[Luccas]

Good night,


Last week I begun to study differential equations by my own and first saw ODE's of separable variables. I've learned very well what they are and how to find constant and non-constant solutions. But something extremely trivial is boring me: I can't figure out why some ODE is or is not of separable variable. For example, I know that an ODE of s.v. is an ODE of the type

[; \frac{dx}{dt} = g(t)h(x) ;]​

but I simply cannot say why

[; \frac{dy}{dx}=\frac{y}{x} ;]​

is and ODE of s.v. and why

[; \frac{dy}{dx}=\frac{x+y}{x^2 +1} ;]​

is not.

I know this is very trivial and I am missing something, but I don't know what. Can you help me, please? :-)


[]'s!

Ps.: sorry for my lousy English.