king9312
May 28, 2015, 6:28am
1
Hello,
I am a new user of Mathematica and I have a problem solving a no linear equation:
(E^(-2 Sqrt[
20 - 2 p]) (-2 Sqrt[-(-10 + p) p]
Sin[Sqrt[2] Sqrt[p]]^2 - (-10 + p) Sin[2 Sqrt[2] Sqrt[p]]))/p
It’s a little bit complicated. I try using Solve, and other package to find roots that I found in internet. I know that I can solve it using FindRoot but I want all the possible solution to it.
I try programming a cycle to evaluate point by point but It doesn’t work. I traying to solve for p
Can you help me?
Greetings
Luis
For this type of non-linear equation, best to use FindRoot as follows:
In[22]:= FindRoot[eq, {p, 1.}]
Out[22]= {p -> 0.81974}
In[25]:= Plot[Evaluate[eq[[1]]], {p, 0, 2}]
The solution is also apparent from the plot:
For this type of non-linear equation, best to use FindRoot as follows:
In[22]:= FindRoot[eq, {p, 1.}]
Out[22]= {p -> 0.81974}
In[25]:= Plot[Evaluate[eq[[1]]], {p, 0, 2}]
The solution is also apparent from the plot:
More roots can be found:
In[30]:= eq = (E^(-2 Sqrt[
20 - 2 p]) (-2 Sqrt[-(-10 + p) p] Sin[
Sqrt[2] Sqrt[p]]^2 - (-10 + p) Sin[2 Sqrt[2] Sqrt[p]]))/
p == 0;
In[31]:= FindRoot[Evaluate[eq], {p, 6}]
Out[31]= {p -> 4.9348}
In[32]:= FindRoot[Evaluate[eq], {p, 7.}]
Out[32]= {p -> 6.94577}
NSolve also can.
sol = NSolve[(E^(-2 Sqrt[
20 - 2 p]) (-2 Sqrt[-(-10 + p) p] Sin[
Sqrt[2] Sqrt[p]]^2 - (-10 + p) Sin[2 Sqrt[2] Sqrt[p]]))/
p == 0, p, Reals] // Quiet; p /. sol
Output: {0.81974, 4.9348, 6.94577, 10.}
