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Question: why odetest no longer verify solution after expanding it?

Question:why odetest no longer verify solution after expanding it?

nm 8552 Maple 2019
simplify expand trigonometry differential-equations odetest
September 08 2019
0

Is this documented somewhere?  Why Maple do not return 0 from odetest after expanding the solution?

update: added additional tries to simplify it to zero as suggested but they do not give zero.

> 

ode:=2*x^(1/2)*diff(y(x),x) = (1-y(x)^2)^(1/2);
sol:=dsolve(ode);

2*x^(1/2)*(diff(y(x), x)) = (1-y(x)^2)^(1/2)

y(x) = sin(x^(1/2)+(1/2)*_C1)

> 

odetest(sol,ode);

0

> 

res:=odetest(expand(sol),ode);

cos(x^(1/2)+(1/2)*_C1)-(1/2)*(2*cos(2*x^(1/2)+_C1)+2)^(1/2)

> 

simplify(res)

cos(x^(1/2)+(1/2)*_C1)-(1/2)*(2*cos(2*x^(1/2)+_C1)+2)^(1/2)

> 

simplify(res,symbolic)

cos(x^(1/2)+(1/2)*_C1)-(1/2)*(2*cos(2*x^(1/2)+_C1)+2)^(1/2)

> 

simplify(res,trig)

cos(x^(1/2)+(1/2)*_C1)-(1/2)*(2*cos(2*x^(1/2)+_C1)+2)^(1/2)

> 

combine(res)

cos(x^(1/2)+(1/2)*_C1)-(1/2)*(2*cos(2*x^(1/2)+_C1)+2)^(1/2)

> 

combine(res,trig)

cos(x^(1/2)+(1/2)*_C1)-(1/2)*(2*cos(2*x^(1/2)+_C1)+2)^(1/2)

> 

expand(res)

cos(x^(1/2))*cos((1/2)*_C1)-sin(x^(1/2))*sin((1/2)*_C1)-(1/2)*(4*cos(_C1)*cos(x^(1/2))^2-2*cos(_C1)-4*sin(_C1)*sin(x^(1/2))*cos(x^(1/2))+2)^(1/2)

> 

simplify(expand(res))

cos(x^(1/2))*cos((1/2)*_C1)-sin(x^(1/2))*sin((1/2)*_C1)-(1/2)*(4*cos(_C1)*cos(x^(1/2))^2-2*cos(_C1)-4*sin(_C1)*sin(x^(1/2))*cos(x^(1/2))+2)^(1/2)

> 

simplify(expand(res),symbolic)

cos(x^(1/2))*cos((1/2)*_C1)-sin(x^(1/2))*sin((1/2)*_C1)-(1/2)*(4*cos(_C1)*cos(x^(1/2))^2-2*cos(_C1)-4*sin(_C1)*sin(x^(1/2))*cos(x^(1/2))+2)^(1/2)

> 

simplify(expand(res),trig)

cos(x^(1/2))*cos((1/2)*_C1)-sin(x^(1/2))*sin((1/2)*_C1)-(1/2)*(4*cos(_C1)*cos(x^(1/2))^2-2*cos(_C1)-4*sin(_C1)*sin(x^(1/2))*cos(x^(1/2))+2)^(1/2)

> 

simplify(expand(res),size)

cos(x^(1/2))*cos((1/2)*_C1)-sin(x^(1/2))*sin((1/2)*_C1)-(1/2)*(4*cos(_C1)*cos(x^(1/2))^2-2*cos(_C1)-4*sin(_C1)*sin(x^(1/2))*cos(x^(1/2))+2)^(1/2)

> 

 

 

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