Using eval undefined function or variable

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So I have a exercise to solve a differential equation and I have to use Pikar's method to draw some of the approximations.However I have trouble using eval. Here is my code:
function ex1
hold on;
grid on;
xmin=1;xmax=3;
x0=2;y0=2;
axis([xmin xmax -1,5]);
y=dsolve('Dy=x*(3*y-2)*sin(1-4*x^2)','y(2)=2','x')
t=xmin:(xmax-xmin)/100:xmax;
plot(t,eval(y),'k');
function z = ff(x,y)
z=x.*(3*y-2).*sin(1-4*(x.^2));
end
% Calculating the approximations
X=xmin:(xmax-xmin)/100:xmax;
Y=y0*ones(1,length(X));
plot(X,Y,'y');
Z=Y;
N=8;
for k=1:N
YK=y0+cumtrapz(X,ff(X,Z));
if(k==1)
plot(X,Y,'g');
elseif(k==2)
plot(X,Z,'b');
elseif(k==7)
plot(X,Z,'r');
end
Z=YK;
end
end
And the errors I am getting are :
Error using evalin
Undefined function or variable 'x'.
Error in sym/eval (line 11)
s = evalin('caller',vectorize(map2mat(char(x))));
Error in ex1 (line 12)
plot(t,eval(y),'k');

Accepted Answer

Walter Roberson
Walter Roberson on 7 Jan 2018
Do not eval() a symbolic expression. Symbolic expressions are in a language that is not MATLAB and is not MUPAD.
The result of the dsolve is the symbolic expression
(4*exp(-(3*cos(15))/8)*exp((3*cos(4*x^2 - 1))/8))/3 + 2/3
When you try to eval() that, you need to have a variable named x defined, but you do not.
sol = double( subs(y, sym('x'), t) );
plot(t, sol)

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