Advanced Search

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

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

nm 9889 Maple 2024
solve lambertw
June 12 2024
2

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?
 

15172

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

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]);

((a^2-4*b*y)^(1/2)-a*ln(a+(a^2-4*b*y)^(1/2)))/b = x+c__1

(-(a^2-4*b*y)^(1/2)-a*ln(a-(a^2-4*b*y)^(1/2)))/b = x+c__1

(1/5)*(-20*y+1)^(1/2)-(1/5)*ln(1+(-20*y+1)^(1/2)) = x+2

-(1/5)*(-20*y+1)^(1/2)-(1/5)*ln(1-(-20*y+1)^(1/2)) = x+2

> 

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

-(1/20)*LambertW(-exp(-11-5*x))*(LambertW(-exp(-11-5*x))+2)

> 

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

-(1/20)*LambertW(-exp(-11-5*x))*(LambertW(-exp(-11-5*x))+2)

> 

eval(sol1,x=10.);

0.3221340286e-27

> 

eval(sol2,x=10.);

0.3221340286e-27

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]);

((a^2-4*b*y)^(1/2)-a*ln(a+(a^2-4*b*y)^(1/2)))/b = x+c__1

(-(a^2-4*b*y)^(1/2)-a*ln(a-(a^2-4*b*y)^(1/2)))/b = x+c__1

(1/5)*(-20*y+1)^(1/2)-(1/5)*ln(1+(-20*y+1)^(1/2)) = 12

-(1/5)*(-20*y+1)^(1/2)-(1/5)*ln(1-(-20*y+1)^(1/2)) = 12

> 

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

-205.8850616

> 

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

0.3221340286e-27


 

Download different_equations_give_same_solution_june_12_2024.mw

 
Please Wait...