It‘s really the simplest way I've ever seen to solve this kind of equation!

@Preben Alsholm 

Solving for a and b.

@mattcanderson1 

I've never sent any email to you and been totally surprised by your reply. 

@Markiyan Hirnyk 

Thanks for your reply!

“x” has been assigned in a not so obvious way that I hadn’t realized before. 

But there isn't any expression for x at all!

@itsme 

 Thanks so much for your timely reply!

It works when replaced by Pi!

@Axel Vogt 

The problem still remains,

Code:

sin((1/10)*pi);
convert(%, radical);

@Alejandro Jakubi 

Thanks so much for your Wonderful Reply!！

Yeah, the old version I refer to is Maple V.

Glad to see you again!

You’re really so familiar with the Maple, and I deem you should be entitled with MVP!

@Axel Vogt 

Thanks so much for your reply！

But for sin（pi/4）, sin（pi/3）and so on, Maple will directly return radicals.

PS, I thought the code was very short, so I didn’t post it. Next time, I’ll post it, no matter how short it is.

@Alejandro Jakubi 

Thanks so much for your insightful reply!

Let's hope these two bugs can be fixed in the next version of Maple--Maple 19.

@ecterrab 

Thanks so much for your Excellent Reply!

@Markiyan Hirnyk 

PS，I deem in mathematics, the neighborhood of the origin contains the origin itself. 

@Markiyan Hirnyk 

The original ODE doesn’t have any singularity at the origin, but has a branch at t=0 instead.

@Markiyan Hirnyk 

The “first form” here simply means the form of the ODE before your“not”, while the ”second form” means the one after it.

 Even if we adopted your “good” form, we would still get the same error, just as below:

By the way, here is the plaintext of the code, you can copy and paste them to check it out by yourself :

solve({U(0) = 0, diff(U(t), t) = (2*(sqrt(U__0)-sqrt(U(t))))*sqrt(U(t))})

@Markiyan Hirnyk 

 With all due respect, I’m afraid any textbooks on calculus(no matter elementary, intermediate or advanced) would suggest that the first form you’ve mentioned is the correct equivalence to my ODE while the second is wrong, so there is no singularity at the neighborhood of the origin.