In this ODE

dsolve gives 

When A=3 but  not when A=1 or A=2

restart;
ode:=(1+y(x))*diff(y(x),x$2)-A*diff(y(x),x)^2=x;
A:=1;
dsolve(ode):
A:=2;
dsolve(ode):
A:=3;
dsolve(ode):

The problem is not with the particular solution. Maple can find that

DEtools:-particularsol(ode,y(x))

And it can solve the homogeneous ODE for any A:

restart;
ode:=(1+y(x))*diff(y(x),x$2)-A*diff(y(x),x)^2=0;
A:=1;
dsolve(ode):
A:=2;
dsolve(ode):
A:=3;
dsolve(ode);

Is this a known issue and why it happens on some values?

Maple 2020.1 and Physics 861 on windows 10

When translating initial conditions, for derivatives, to Latex, the output is not easy to read, and was wondering how to make it more standard.

For example, let say initial conditions for second order ODE are [y(0)=0,D(y)(0)=3] in Maple syntax.  I convert these to Latex using

restart;
ic:=[y(0)=0,D(y)(0)=3];
Physics:-Latex(ic)

which gives

               [y \left(0\right) = 0, D\left(y \right)\left(0\right) = 3]

The problem is with derivatives. They are hard to read, unless someone knows Maple. The above renders are

I'd like to get the above to standard form 

Which more easily understood and is the standard in textbooks and papers.

This issue does not show up in Mathematica, because in Mathematica initial conditions can be entered as  {y[0]==0,y'[0]==3} and this translates directly as is

Which renders a

I know in Maple document mode, 2D math input, one can also enter the IC the same as with Mathematica, which is easier, but the Latex translation still the same as with the worksheet 1-D math.

Going back to Maple, I could enter the initial conditions instead as follows

restart;
ic:=[y(0)=0,eval(diff(y(x),x)=3,x=0)];
Physics:-Latex(ic)

And now the latex generated renders as

Which might be more understandble but too heavy weight compared to the simpler form y'(0)=3 and I remember reading that use eval() as above is not as safe as using the D(y)()... notation for initial conditions.

Are there any other tricks that would allow the latex of derivative to show in the standard form to make it easier to read?

Is it possible for Physics:-Latex to automatically detect the form D(y)(x0)=y0 and generate y'(x0)=y0 for its Latex? This will be the ideal solution. This will apply to higher derivatives as well. For example 

Physics:-Latex( (D@@2)(y)(0)=3)

Now gives

         D^{\left(2\right)}\left(y \right)\left(0\right) = 3

which renders as

While a much better output would be the standard

This will go a long way towards improving the Latex generated by Maple.

Any suggestions?

This is really a math question. But I can't figure how Maple did it.

Maple solves the ODE with 2 initial conditions correctly.

But if I use the general solution, and setup the set 2 equations, and tell Maple to solve _C1 and _C2, it says there is no solutions. Which is correct.

I would really like to know how Maple then managed to solve for these initial conditions.  This is problem from text book

I know how to solve it by hand to obtain general solution. But do not know how find solution that satisfies the IC's. when pluggin the initial conditions, the resulting 2 equation have no solution.

restart;
ode:=2*diff(y(x),x$2)=exp(y(x));
maple_general_sol:=dsolve(ode);
odetest(maple_general_sol,ode);
IC:=y(0)=0,D(y)(0)=1;
maple_sol_with_IC:=dsolve([ode,IC]);
odetest(maple_sol_with_IC,[ode,IC]);

The goal is to now take the general solution found by Maple above, and manually solve for _C1 and _C2:

eq1:=0=subs(x=0,rhs(maple_general_sol));
the_derivative:= diff(rhs(maple_general_sol),x):
eq2:=1=subs(x=0,the_derivative);

Two equations, two unknown. But using solve or PDEtools:-Solve produce no solution.

sol1:=solve([eq1,eq2],[_C1,_C2]);
sol2:=PDEtools:-Solve([eq1,eq2],[_C1,_C2]);

Looking at equation (1) above, we see that it is the same as 

eq1:=1=(tan(_C2/(2*_C1))^2 + 1)/_C1^2;

Because 0=ln(Z) means Z=1. Using the above simpler equation now gives

eq1:=1=(tan(_C2/(2*_C1))^2 + 1)/_C1^2;
the_derivative:= diff(rhs(maple_general_sol),x):
eq2:=1=subs(x=0,the_derivative);
sol1:=solve([eq1,eq2],[_C1,_C2]);

We see that there is indeed no solution. Second equation above says _C1= tan(.). Let tan(.)=Z. Plugging this in first equation gives Z^2= (Z^1+1) which has no solution for Z since this says 0=1 

So direct appliction of the initial conditions produces no solution. So how did Maple find the solution it obtained? I also tried using limits. But no luck. Book does not show how to obtain solution either. 

Any ideas?

When solving this by hand   sqrt(y)=tanh(x), I would square both sides to obtain  y=tanh(x)^2 as solution.  

Maple does this when RHS is tan,cos,sin, but not when RHS is hyperbolic.

Why is that, and how to best tell Maple to give  the simple solution? Here is an example

restart;
eq:=sqrt(y)=tanh(x);
sol:=solve(eq,y);

Compare to Mathematica:

I can post-process Maple solution like this

restart;
eq:=sqrt(y)=tanh(x);
sol:=solve(eq,y);
sol:=convert(sol,trigh);
sol:=simplify(sol)

Which is tanh(x)^2.  

But this is all too much work, since this is done in a program, and I do not know what specific convert to use at the time to try.

My question is, why does not maple simply solves   sqrt(y) = f(x)  giving     y=f(x)^2?  it works for generic function

restart;
eq:=sqrt(y)=f(x);
sol:=solve(eq,y);

it works for non-hyper trig functions also

restart;
eq:=sqrt(y)=tan(x);
sol:=solve(eq,y);

Is there a trick to make it work for hyperbolic functions also automatically?

ps. for now, to avoid all these issues, I am doing this

restart;
the_rhs:=tanh(x);
eq:=sqrt(y)=f;
sol:=solve(eq,y);
sol:=subs(f=the_rhs,sol);

Since I know that the RHS contains no y before hand. The above bypasses any issues Maple has with hyper trig functions.

When Maple converts a matrix or a vector to Latex it uses latex array, which  is fine, but what it does is insert an exatra \\ at the end of the last row, just before the \end{array} 

This causes problem for some software which reads the latex file. It causes the software to take this as empty row and inserts a blank row at the end.

Here is a small example

A:=Matrix([[1,2],[3,4]]);
Physics:-Latex(A);

              \left[\begin{array}{cc}1 & 2 \\3 & 4 \\\end{array}\right]

Notice the extra \\  just before the \end{array} In Latex, this tells latex compiler to insert newline basically.

When opening the latex file using external software, which reads Latex and converts it to GUI, it show this

And now I have to go edit the latex by hand removing the extra \\ (inside the editor I can do global search and replace)

A better outout from Maple's Latex command would be the following

\left[\begin{array}{cc}1 & 2 \\3 & 4 \end{array}\right]

Even though both are valid Latex, the above is better.  I was wondering how hard it is to do this change.

All what the conversion needs to do is just check if the row in the matrix (or Vector) is the last one, and omit the extra \\ at the end of the last row. That is all. 

I could ofcourse write code to try to parse this each time I call Latex and to remove \\ myself in the program, but it will be much easier if Maple automatically did this.

ps. if the Latex conversion source code could be made public, others could help make improvement to it for free, benefiting Maple and everyone using it. Maplesoft would still approve the changes before checkin, and retain the copy right of the source code ofcourse. 

Maple 2020.1