Why does "solve" throw an error when I try to solve a simple equation containing an integral in MATLAB?

I am getting an error when trying to solve the very simple equation:

 

       y + y*I == 0

 

where "I" is an integral that does not depend on "y":

>> syms x
>> I = int(-(1+1/x)*exp(-1/2*log(x)^2), x, 0.01, 1);

>> syms y
>> solve(y + I*y == 0, y)

Error using mupadengine/feval (line 157)

MuPAD error: Error: The second argument must be of form x or x = a..b. [int]

 Error in *solve* (line 170)
   sol = eng.feval('symobj::solvefull',eqns,vars);

 

Is this a bug?

Also, how can I solve the same equation in case the integral depends on the unknown "y"? For example:

       syms x y
       f = y + int(-exp(-log(x)^2/2)*(y+ y/x), x, 0.01,1);

Answer 1

[MathWorks Support Team]

There is a bug in the Symbolic Math Toolbox that affects release R2014a and prior. The bug causes the "int" function to return an invalid syntax -- it is a mix of MuPAD and MATLAB syntax. Thus, the "solve" function thinks that "x" is an unknown and cannot solve the equation.

  1. If the integral is a constant

As a workaround, if integral "I" is a constant, you can numerically approximate its value using the "vpa" function:

>> syms x
>> I = int(-(1+1/x)*exp(-1/2*log(x)^2), x, 0.01, 1);

>> syms y
>> solve(y + vpa(I)*y == 0, y)

ans =

0

  2. If the integral depends on the unknown

If integral "I" depends on "y", you can use the MuPAD "simplify" and "solve" functions with "feval" as follows:

>> syms x y
>> f = y + int(-exp(-log(x)^2/2)*(y+ y/x), x, 0.01,1);
>> simplify(feval(symengine, 'solve', f, y))

ans =

0