Which type differential equation is this?

[Susanne217]

Which type differential equation is this??

I simply can't recognize it


$$y' = \frac{1}{3}y^{\frac{1}{2}} + t^{\frac{1}{3}}$$

Which type of differential equation is??

non-linear?

 

[Mark44]

First order, nonlinear.

 

[Susanne217]

First order, nonlinear.

Hi and thank you for your answer...

which method do I use to solve this? integration factor? or separation of the variables?

I keep ending wrong result :(

So if you could point me direction of the right method to solve it. That would be nice :)

 

[jackmell]

So if you could point me direction of the right method to solve it. That would be nice :)

It's non-linear and often these require special techniques to solve. Integration factor is usually used for linear equations and this one can't be separated. This is what I usually do: try a bit to solve it by hand. I did that and got nothing. My next approach is to use DSolve in Mathematica:

DSolve[y'[t] == 1/3 y[t]^(1/2) + t^(1/3), y, t]

At least that way, if Mathematica gives me a solution, I know it's relatively easy to solve and the exact form of the answer often gives me a hint on how to solve it. However in this case Mathematica can't solve it. At that point, I think it's probably not easy to solve symbolically although sometimes Mathematica is in error. I may or may not look in a DE handbook. Sometimes that's helpful. Finally, my next approach would be to use NDSolve in Mathematica and solving it (an IVP) numerically and if necessary, fit a curve to the data if some approx. symbolic representation is sufficient.

 

[Susanne217]

It's non-linear and often these require special techniques to solve. Integration factor is usually used for linear equations and this one can't be separated. This is what I usually do: try a bit to solve it by hand. I did that and got nothing. My next approach is to use DSolve in Mathematica:

DSolve[y'[t] == 1/3 y[t]^(1/2) + t^(1/3), y, t]

At least that way, if Mathematica gives me a solution, I know it's relatively easy to solve and the exact form of the answer often gives me a hint on how to solve it. However in this case Mathematica can't solve it. At that point, I think it's probably not easy to solve symbolically although sometimes Mathematica is in error. I may or may not look in a DE handbook. Sometimes that's helpful. Finally, my next approach would be to use NDSolve in Mathematica and solving it (an IVP) numerically and if necessary, fit a curve to the data if some approx. symbolic representation is sufficient.

I get a solution in Maple, but it very strange containing integral sign etc. There must be away to solve this equation without having to use computeral power. Hallsofty we need your guidence Master Science Jedi...

 

[jackmell]

Hallsofty we need your guidence Master Science Jedi...

Agreed, but I would say just "Master Jedi".

 

[JJacquelin]

Hi Guys !

I am not a Jedi, so I let the most honorific job for them.
I did only a subaltern job which consists in expressing the result in terms of series development.
To be honest, I confess that my devoted computer did the even more subaltern work, which in fact is almost the whole, while I had a drink.
Well, have a look at the joint document.

 

[jackmell]

Wait, let me check . . . yep, that's you alright. Startin' to look like it to me. Anyway, that's really nice Jacquelin. I think it would be nice to verify that solution, say numerically to some acceptable level of precision. And how does one compute the radius of convergence? I have problems figuring that out when a Cauchy product is involved.