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Question: odetest problem verifying same solution

Question:odetest problem verifying same solution

nm 9668
odetest
August 07 2016
1

Give this

ode:=diff(y(x),x)=a*cos(y(x))+b;
sol_1:=2*arctan( (a+b)/sqrt(b^2-a^2) * tan(1/2*sqrt(b^2-a^2)*(x+_C1)));
sol_2:=2*arctan( sqrt(a+b)/sqrt(b-a) * tan(1/2*sqrt(b^2-a^2)*(x+_C1)));

sol_1 and sol_2 are the same. Only difference is that I wrote  (a+b)/sqrt(b^2-a^2) in one, and  sqrt(a+b)/sqrt(b-a) in the other. But these two expressions are the same. But odetest gives zero on the first and not on the second:

odetest(y(x)=sol_1,ode);
       0

odetest(y(x)=sol_2,ode);
       not zero 

Why did Maple not verify sol_2?

Maple 2016.1 on windows 7

 
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