How to obtain this solution using dsolve?

Question:How to obtain this solution using dsolve?

Posted: nm 11398 Product: Maple 2025

2 hours ago

Maple 2025.1 unable to solve this ode. Sympy gives the following two solutions which Maples verifies are correct.

Any trick or option that can help dsolve find these solutions?

>	interface(version);

restart;

>	ode:=diff(y(x),x) = (1+cos(x)sin(y(x)))tan(y(x));

>	sol:=dsolve(ode);

>	sol_1:=y(x)=arcsin( 2exp(x) / ( c__1 + sqrt(2)exp(x) * sin(x+Pi/4) ) ) + Pi

y(x) = arcsin(2*exp(x)/(c__1+2^(1/2)*exp(x)*sin(x+(1/4)*Pi)))+Pi

>	odetest(sol_1,ode)

>	sol_2:=y(x)=arcsin( 2exp(x) / ( c__1 - sqrt(2)exp(x) * sin(x+Pi/4) ) ) ;

y(x) = arcsin(2*exp(x)/(c__1-2^(1/2)*exp(x)*sin(x+(1/4)*Pi)))

>	odetest(sol_2,ode)

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