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Question: why odetest fail to verify solution when using C[1] instead of _C1 as constant of integration?

Question:why odetest fail to verify solution when using C[1] instead of _C1 as constant of integration?

nm 8552 Maple 2019
differential-equations odetest
August 29 2019
1

Why odetest sometimes fail to give 0  from odetest when simply using C[1] instead of _C1 as constant of integration?

I do not remember now if I asked about this before now. But for me as a user, this does not look right. I like to use C[1] instead of _C1 as the constant of integration as it looks better in Latex. I had no idea it will make a difference to odetest what the constant of integration symbol used is.

Is this a known issue? Do you consider this a bug? Maple 2019.1 on windows 10.

> 

restart;
> 

ode:= x^2*diff(y(x),x)+x*y(x)+sqrt(y(x)) = 0;

x^2*(diff(y(x), x))+x*y(x)+y(x)^(1/2) = 0

> 

sol_1:=sqrt(y(x))=1/x+_C1/sqrt(x);
odetest(sol_1,ode)

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

0

> 

sol_2:=subs(_C1=C[1],sol_1);
odetest(sol_2,ode); #why this now fails??

y(x)^(1/2) = 1/x+C[1]/x^(1/2)

-y(x)^(1/2)-y(x)^(1/2)*x^(1/2)*C[1]+x*y(x)

> 

sol_3:=subs(C[1]=_C1,sol_2);
odetest(sol_3,ode)

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

0

 

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