# Question:why Maple gives same solution for two different equations?

## Question:why Maple gives same solution for two different equations?

Maple 2024

Maple gives same solution for two different equations.

```eq1 := 1/5*sqrt(-20*y + 1) - 1/5*ln(1 + sqrt(-20*y + 1)) = x + 2;
eq2 := -1/5*sqrt(-20*y + 1) - 1/5*ln(1 - sqrt(-20*y + 1)) = x + 2;```

Solving these for y, gives same exact solution. But this is not correct. As this worksheet shows.

Is this a bug? How could two different equations give same solution?

 > interface(version);

Case 1. Solve first then plugin x value in solution

 > eq1:=(sqrt(a^2 - 4*b*y) - a*ln(a + sqrt(a^2 - 4*b*y)))/b=x+c__1; eq2:=(-sqrt(a^2 - 4*b*y) - a*ln(a - sqrt(a^2 - 4*b*y)))/b=x+c__1; eq1:=eval(eq1,[a=1,b=5,c__1=2]); eq2:=eval(eq2,[a=1,b=5,c__1=2]);

 > sol1:=simplify(solve(eq1,y));

 > sol2:=simplify(solve(eq2,y));

 > eval(sol1,x=10.);

 > eval(sol2,x=10.);

Case 2. Plugin in same x value in equation and then solve, we get different answers

 > eq1:=(sqrt(a^2 - 4*b*y) - a*ln(a + sqrt(a^2 - 4*b*y)))/b=x+c__1; eq2:=(-sqrt(a^2 - 4*b*y) - a*ln(a - sqrt(a^2 - 4*b*y)))/b=x+c__1; eq1:=eval(eq1,[a=1,b=5,c__1=2,x=10]); eq2:=eval(eq2,[a=1,b=5,c__1=2,x=10]);

 > sol1:=evalf(solve(eq1,y));

 > sol2:=evalf(solve(eq2,y));

Download different_equations_give_same_solution_june_12_2024.mw

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