Differential Equation Error: "Warning: Unable to find explicit solution"

Question

Michael Bortolot 2019-4-23

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回答： Om Yadav 2020-4-24

Hi Guys,

I'm trying to solve a system of differential equations using matlab. Here is my code (take out the beginning and ending paranthesis):

clc;clear all
syms x1(t) x2(t) x3(t)
A=[-(.0211*heaviside(t-500)+.2111*heaviside(t-500)+.015)*(x1) .0111*(x1) .0039*(x1); 0.0124*(x2) -.0286*(x2) 0; 0.000035*(x3) 0 -.000035*(x3)];
B=[49.3; 0; 0];
Y=[x1(t); x2(t); x3(t)]
odes = diff(Y) == A*Y + B
[x1Sol(t), x2Sol(t), x3Sol(t)] = dsolve(odes);
x1Sol(t) = simplify(x1Sol(t))
x2Sol(t) = simplify(x2Sol(t))
x3Sol(t) = simplify(x3Sol(t))
C = Y(0) == [0; 0; 0];
[x1Sol(t), x2Sol(t), x3Sol(t)] = dsolve(odes,C)
for i=1:800
    x1(i)=x1Sol(i)
    x2(i)=x2Sol(i)
    x3(i)=x3Sol(i)
end
hold on 
plot(x1)
plot(x2)
plot(x3)
hold off
clearvars
ylabel('Micrograms of Lead')
xlabel('Number of Days')
legend('Amount in Blood', 'Amount in Tissue', 'Amount in Blood')"

I keep getting the following error message:

Warning: Unable to find explicit solution.

> In dsolve (line 201)

In MathFinal4 (line 8)

Error using sym/subsindex (line 845)

Invalid indexing or function definition. Indexing must follow MATLAB indexing. Function arguments must

be symbolic variables, and function body must be sym expression.

Error in MathFinal4 (line 8)

[x1Sol(t), x2Sol(t), x3Sol(t)] = dsolve(odes);

Please Help!

I can't seem to fix this problem no matter how I arrange the differential equation (I've tried standard form and matrix form),

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Star Strider 2019-4-24

Your system is nonlinear so an analytic solution is not possible. Although odeToVectorField correctly transforms it, the heaviside calls prevent matlabFunction from creating an anonymous function for it.

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Answer 1

Sulaymon Eshkabilov 2019-5-4

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Hi,

Since you have the Step function, one of the most suitable Symbolic MATH toolbox functions for this type of ODEs is the Laplace transform and its inverse via laplace() and ilaplace()