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These are questions asked by Ratch


I tried the video example of the Explorer Assistant, and get jumbled output.  See the *.mw file.



Can anyone tell me how to solve the equation above using Maple.  I know that there is a solution around x=0.995, y=0.743, but I cannot induce Maple to find it.  Any help or suggestions would be appreciated.



Can anyone tell me how to use dsolve to find the solution to the problem in the attachment.  It is faily easy to do using substitution for homogeneous coefficients, but dsolve seems to put out a very complicated solution to the problem.


2*x*y(x)+(x^2+y(x)^2)*(diff(y(x), x))

2*x*y(x)+(x^2+y(x)^2)*(diff(y(x), x))



y(x) = ((1/2)*(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3)-2*x^2*_C1/(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3))/_C1^(1/2), y(x) = (-(1/4)*(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3)+x^2*_C1/(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3)-((1/2)*I)*3^(1/2)*((1/2)*(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3)+2*x^2*_C1/(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3)))/_C1^(1/2), y(x) = (-(1/4)*(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3)+x^2*_C1/(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3)+((1/2)*I)*3^(1/2)*((1/2)*(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3)+2*x^2*_C1/(4+4*(4*x^6*_C1^3+1)^(1/2))^(1/3)))/_C1^(1/2)




Download DEprob.mw

     Many times when I use dsolve to find the solution of an equation like x-y/y' = y , I get a term involving the LambertW function.  However, the equation has homogeneous coefficients for dx and dy, so it can easily be solved by substituting y=u*x and separating the variables.  The closed form solution of the above is x+y*ln(y)+c*y = 0 , but I cannot get that answer from Maple.  Is there...

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