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Solving Equations 19

sol =
x: [2x1 sym]
y: [2x1 sym]

To see the vectors of x and y values of the solution, type sol.x and sol.y.To
see the individual values, type sol.x(1), sol.y(1), etc.
Some equations cannot be solved symbolically, and in these cases solve
tries to ﬁnd a numerical answer. For example,

>> solve(’sin(x) =2-x’)

ans =
1.1060601577062719106167372970301

Sometimes there is more than one solution, and you may not get what you
expected. For example,

>> solve(’exp(-x) = sin(x)’)

ans =
-2.0127756629315111633360706990971
+2.7030745115909622139316148044265*i

The answer is a complex number; the i at the end of the answer stands for
√
the number −1. Though it is a valid solution of the equation, there are also
real number solutions. In fact, the graphs of exp(−x) and sin(x) are shown in
Figure 2-3; each intersection of the two curves represents a solution of the
equation e −x = sin(x).
You can numerically ﬁnd the solutions shown on the graph with fzero,
which looks for a zero of a given function near a speciﬁed value of x. A solution
of the equation e −x = sin(x) is a zero of the function e −x − sin(x), so to ﬁnd the
solution near x = 0.5 type

>> fzero(inline(’exp(-x) - sin(x)’), 0.5)

ans =
0.5885
Replace 0.5 with 3 to ﬁnd the next solution, and so forth.

In the example above, the command inline, which we will discuss further in
the section User-Deﬁned Functions below, converts its string argument to a

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