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I want to solve this differential equation using Mathematica:

de[r_]= [(-6 r+(-7+θ) ρ[r] (ρ^′)[r]) (1+(ρ^′)[r]^2)+r ρ[r] (ρ^′′)[r]
DSolve[de[r_]==0,r,ρ[r]]

which is not working. is there other way to solve this?

agentp
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M.R. H.Loo
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  • This `de[r_]:=((-7+θ)ρ[r] ρ'[r])(1+ρ'[r]^2)+r ρ[r] ρ''[r]; DSolve[de[r]==0,ρ[r],r]` solves instantly. Adding the -6r in front seems to stun it. If you could provide initial conditions this might help. If you could also assign a constant numeric value to θ then you would be able to try using `NDSolve`. – Bill Oct 03 '17 at 00:06
  • you really need to take some time to learn the basic syntax. Square brackets are not used for grouping in mathematica. What is `p^''`, supposed to be?? – agentp Oct 03 '17 at 02:39
  • Thank you for your answer. Is there another way to solving the differential equation without changing it? – M.R. H.Loo Oct 03 '17 at 15:27
  • Make sure your input is exactly correct and then let MMA grind on it for a few weeks on a computer with LOTS of memory and see if it ever finds a solution. I do not know if there is any closed form solution or any MMA can ever find. You might try a series solution like this https://mathematica.stackexchange.com/questions/25363/solving-an-ode-in-power-series using something like this odeOperator = ((-7+ϑ) # D[#,r])(1+D[#,r]^2)+r # D[#,{r,2}]&; xx=Series[ρ[r], {r,0,3}]; soln = Simplify[SolveAlways[odeOperator[ xx]==0,t]] I do not know if that will work without any initial conditions. – Bill Oct 03 '17 at 17:37

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