Symbolic Math Toolbox

Solving Equations

Solving Algebraic Equations

If S is a symbolic expression,

• solve(S)
  

attempts to find values of the symbolic variable in S (as determined by findsym) for which S is zero. For example,

• syms a b c x
  S = a*x^2 + b*x + c;
  solve(S)
  

uses the familiar quadratic formula to produce

• ans =
  [1/2/a*(-b+(b^2-4*a*c)^(1/2))]
  [1/2/a*(-b-(b^2-4*a*c)^(1/2))]
  

This is a symbolic vector whose elements are the two solutions.

If you want to solve for a specific variable, you must specify that variable as an additional argument. For example, if you want to solve S for b, use the command

• b = solve(S,b)
  

which returns

• b =
  -(a*x^2+c)/x
  

Note that these examples assume equations of the form . If you need to solve equations of the form , you must use quoted strings. In particular, the command

• s = solve('cos(2*x)+sin(x)=1')
  

returns a vector with four solutions.

• s =
  [      0]
  [     pi]
  [ 1/6*pi]
  [ 5/6*pi]
  

Eigenvalue Trajectories

Several Algebraic Equations