[ylny + e^(-xy)]dx + (1/y - xlny)dy = 0
10 views (last 30 days)
Show older comments
please solve this differential equation or tell me the type.
0 Comments
Answers (1)
Roger Stafford
on 30 Nov 2013
You can attempt to find an explicit solution using 'dsolve'. See its documentation at:
http://www.mathworks.com/help/symbolic/dsolve.html
Presumably you would use something like
dsolve('Dy = (y*log(y)+exp(-x*y))/(x*log(y)-1/y)','x')
or if you want y to be the independent variable
dsolve('Dx = (x*log(y)-1/y)/(y*log(y)+exp(-x*y))','y')
However, there is no guarantee that 'dsolve' would succeed in finding an explicit solution. If not, you would need to solve it numerically using specified initial conditions with one of the ode functions, such as ode45, ode23, ode113, ode15s, etc.
3 Comments
Roger Stafford
on 1 Dec 2013
No, this is an ordinary differential equation of the form
dy/dx = f(x,y)
which can also be written
dx/dy = 1/f(x,y)
It is possible that another parameter, t, could be defined that would simplify matters, but if so I couldn't find one.
Walter Roberson
on 1 Dec 2013
Ah, I see, yes, it can be written
diff(y(x), x) = (y*ln(y)+exp(-x*y))/(-1/y+x*ln(y))
I still don't know how to solve that symbolically, but I do see now that a third variable is not needed to express it.
See Also
Categories
Find more on Ordinary Differential Equations in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!