# Question:why is Maple not able to find solution to this first order ode? Only after adding implicit it can solve it

## Question:why is Maple not able to find solution to this first order ode? Only after adding implicit it can solve it

Maple 2023

This first order ode is quadrature with initial conditions. By existence theorem it has solution and is unique on some interval that includes the initial conditions (because f and f_y  are continuous on the initial condition).

But for some reason Maple can't find the solution, unless one adds 'implicit' option. Why is that? I thought that Maple will automatically return implicit solution if can't find explicit solution.

So does one then needs to try with implicit solution again if no solution is returned? I am basically asking if this is expected behavior of dsolve.

Below is worksheet also with the solution that Maple verifies is valid and satisfies the ode and also initial conditions.

```ode:=diff(y(x), x) = sin(y(x)) + 1;
ic:=y(0)=Pi;
sol:=dsolve([ode,ic]);

```

 > interface(version);

 > Physics:-Version();

 > restart;

 > ode:=diff(y(x), x) = sin(y(x)) + 1; ic:=y(0)=Pi; sol:=dsolve([ode,ic]);

 > maple_sol:=dsolve([ode,ic],'implicit'); odetest(maple_sol,[ode,ic])

 > maple_sol:=dsolve([ode,ic],y(x),'explicit');

 > mysol:=y(x)=2*arccos(-x/(sqrt(4+4*x+2*x^2))); odetest(mysol,[ode,ic]) assuming x>=0

 >