Error using eval with a differential equation

when i do this i get this error:

>> t=0:0.01:10;
>> dsolve('D3x + 6*D2x + 11*Dx + 6*x=6*square(2*pi*t),D2x(0)=0,Dx(0)=0,x(0)=0')
ans =
exp(-t)*int(3*exp(x)*square(2*pi*x), x, 0, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + exp(-3*t)*int(3*exp(3*x)*square(2*pi*x), x, 0, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + exp(-2*t)*int(-6*exp(2*x)*square(2*pi*x), x, 0, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)
>> y=eval(vectorize(ans))
Error using eval
Undefined function or variable 'x'.

what's happening? (i suppose is the square function because if i substitute it for sin(t) it works right.

[Stephen23]

What do you hope to obtain by evaluating the output of dsolve? eval is not the right tool to use:

https://www.mathworks.com/matlabcentral/answers/400718-need-help-with-vector-and-eval#answer_320169

Is there a reason why you are using the very outdated char input to dsolve ?

Answer 1

[Walter Roberson]

Never eval() a symbolic expression. Symbolic expressions are not in the MATLAB language, just in something that is close to the MATLAB language.

But more immediately you need to

syms x

[Stephen23]

jose luis guillan suare's "Answer" moved here:

and how i substitute syms instead of eval in my expresion, thank you.

[Walter Roberson]

t=0:0.01:10;
dsolve('D3x + 6*D2x + 11*Dx + 6*x=6*square(2*pi*t),D2x(0)=0,Dx(0)=0,x(0)=0')
subs(ans)
vpa(ans)

This will take some time, and will produce a useless answer that starts

 [0, ...
  0.99004983374916805357390597718004*numeric::int(3*exp(x)*square(2*pi*x), x == 0..1/100) + 0.97044553354850817693252835195919*numeric::int(3*exp(3*x)*square(2*pi*x), x == 0..1/100) + 0.98019867330675530222081410422531*numeric::int(-6*exp(2*x)*square(2*pi*x), x == 0..1/100), ...
  0.98019867330675530222081410422531*numeric::int(3*exp(x)*square(2*pi*x), x == 0..1/50) + 0.94176453358424870953715278327115*numeric::int(3*exp(3*x)*square(2*pi*x), x == 0..1/50) + 0.96078943915232320943921069132325*numeric::int(-6*exp(2*x)*square(2*pi*x), x == 0..1/50)

Work-around:

syms x(t)
sol = dsolve('D3x + 6*D2x + 11*Dx + 6*x=6*square(2*pi*t),D2x(0)=0,Dx(0)=0,x(0)=0');
Square(t) = piecewise(t - floor(t) < 1/2, 1, -1)
square(t) = Square(t/(2*pi))
T = 0:0.01:10;
solt = vpa(subs(subs(sol), t, T));

This is rather slow. I have evidence at the moment that not all of the values can be resolved to numeric, but I do not yet know which ones.

[Walter Roberson]

Which release are you using by the way? I find that R2017a cannot subs() in the definition of square to the sol, but that R2018a can substitute it.

[jose luis guillan suarez]

and how i plot the equation?

[Walter Roberson]

This is difficult to solve analytically, probably because the differentiation is not all that well defined right at the boundary conditions.

But you can get "good enough" this way:

syms t
Square(t) = piecewise(t - floor(t) < 1/2, 1, -1)
sol_plus = dsolve('D3x + 6*D2x + 11*Dx + 6*x=6*1,D2x(0)=0,Dx(0)=0,x(0)=0');
sol = Square(t) * sol_plus;

This works because solving for =6*-1 gives the negative of sol_plus.

Once you have the above you can plot with

T = 0:0.01:10;
solt = double( subs(sol, t, T) );
plot(T, solt);

Answer 2

[jose luis guillan suarez]

i'm using R2017a