How do I input the below system of equations in Wolfram Alpha in order to solve for the unknowns?
I'm wondering if there's some kind of code that can be written in order to make wolfram alpha understand what I'm talking about.
$$\left.\begin{matrix}
a+b+c+d+e = 0\\
(-a+c+2d+3e) h = 1\\
(a+c+4d+9e)\frac{h^2}{2}= 0\\
(-a+c+8d+27e)\frac{h^3}{6}=0\\
(a+c+16d+81e)\frac{h^4}{24}=0\\
\end{matrix}\right\}$$
I've tried many things already, like
solve{a+b+c+d+f=0, (-a+c+2d+3f)h=1, (a+c+4d+9f)h^2/2=0,
(-a+c+8d+27f)h^3/6=0, (a+c+16d+81f)h^4/24=0,[a,b,c,d,e]}
Thanks for any help.
Best Answer
You have 6 variables but only 5 equations, so there should be a free variable. Mathematica did this just fine for me. What I entered was
Solve[ a + b + c + d + e == 0 && (-a + c + 2 d + 3 e) h == 1 && (a + c + 4 d + 9 e) h^2/2 == 0 && (-a + c + 8 d + 27 e) h^3/6 == 0 && (a + c + 16 d + 81 e) h^4/24 == 0, {a, b, c, d, e, h}]
which gave me the solution
$$a =\frac{-1}{4h},b=\frac{-5}{6h},c=\frac{3}{2h}d=\frac{-1}{2h},e=\frac{1}{12h}$$
with a simple warning. I believe it was just the syntax of how you entered it. Mathematica is a useful tool but is very picky. Their help function always has useful examples and a good place when you have trouble is to start by seeing how they demonstrate approaching things.