Cant Solve ODE with dsolve

Question

Walter Parker 2020-5-14

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/525353-cant-solve-ode-with-dsolve

评论： Bjorn Gustavsson 2020-5-21

采纳的回答： Bjorn Gustavsson

在 MATLAB Online 中打开

I am having issues solving this Differential Equation using dsolve

DEQ:

dT/dt = (A1*exp(1i*(w*t+phi))+A1)*(B1*exp(1i*w*t)-T(t))

CODE:

A1 = 7.9443e-5;
B1 = 10; 
w = 7.3e-5;
phi = 0;
syms T(t)
ode = diff(T) == (A1*exp(1i*(w*t+phi))+A1)*(B1*exp(1i*w*t)-T);
cond = T(0) == 10;
TSol(t) = dsolve(ode,cond);

%The solution comes out to be:
TSol = exp(-(5861854777884531*dt)/73786976294838206464 + ...
    (exp((dt*5386449269523189i)/73786976294838206464)*1953951592628177i)/1795483089841063) * ...
    int((29309273889422655*exp(x*(5861854777884531/73786976294838206464 + ...
    16159347808569567i/147573952589676412928) - ...
    (exp((x*5386449269523189i)/73786976294838206464)*1953951592628177i)/1795483089841063) * ...
    cos((5386449269523189*x)/147573952589676412928))/18446744073709551616, ...
    x, 0, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) + ...
    10*exp(- (5861854777884531*t)/73786976294838206464 + ...
    (exp((t*5386449269523189i)/73786976294838206464)*1953951592628177i)/1795483089841063) * ...
    exp(-1953951592628177i/1795483089841063)

I dont understand what this portion of the solution or the rest of it means.

int((29309273889422655*exp(x*(5861854777884531/73786976294838206464 + 16159347808569567i/147573952589676412928) - (exp((x*5386449269523189i)/73786976294838206464)*1953951592628177i)/1795483089841063)*cos((5386449269523189*x)/147573952589676412928))/18446744073709551616, x, 0, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)

Is it possible for someone to explain why I get (x, 0, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true) in my solution and how do I fix it to get a proper analytical solution. I am running MATLAB R2019a.

I solved a similar differential equation seen below and this work using dsolve so I am not sure why my current DEQ doesn't work:

DEQ: dT/dt = (A1*exp(1i*(w*t+phi)))*(B1*exp(1i*w*t)-T(t))

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Answer 1

Bjorn Gustavsson 2020-5-14

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/525353-cant-solve-ode-with-dsolve#answer_432398

在 MATLAB Online 中打开

So you have a linear first-order differential equation looking something like this:

Then I'd suggest that special cases are combinations of A1 B1 and w equals zero. If I run your code without the numerical values of A1 B1 phi and w I get:

TSol = dsolve(diff(T) == (A1*exp(1i*(w*t+phi))+A1)*(B1*exp(1i*w*t)-T),cond)
TSol =
10*exp(-(A1*exp(phi*1i)*1i)/w)*exp(- A1*t + (A1*exp(phi*1i)*exp(t*w*1i)*1i)/w) + exp(- A1*t + (A1*exp(phi*1i)*exp(t*w*1i)*1i)/w)*int(A1*B1*exp(A1*u + u*w*1i - (A1*exp(phi*1i)*exp(u*w*1i)*1i)/w)*(exp(phi*1i + u*w*1i) + 1), u, 0, t, 'IgnoreSpecialCases', true, 'IgnoreAnalyticConstraints', true)
>> pretty(TSol)
                               t
                               /
   /   A1 #3 1i \             |           /             A1 #3 exp(#1) 1i \
exp| - -------- | #2 10 + #2  |  A1 B1 exp| A1 u + #1 - ---------------- | (exp(phi 1i + #1) + 1) du
   \       w    /            /            \                     w        /
                               0
where
   #1 == u w 1i
            /          A1 #3 exp(t w 1i) 1i \
   #2 == exp| - A1 t + -------------------- |
            \                    w          /
   #3 == exp(phi 1i)

It is a long expression, but it containe nothing extraordinarily complicated, but if for example w is zero this falls appart. You should be able to convert this into a regular m-function in a couple of minutes. It seems to fit the ode rather nicely.

HTH