Explicit solution could not be found.. > In dsolve at 194

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siddharth tripathi 2017-6-1

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https://ww2.mathworks.cn/matlabcentral/answers/342862-explicit-solution-could-not-be-found-in-dsolve-at-194

评论： Star Strider 2017-7-9

采纳的回答： Star Strider

here is my code :

>>sums u(t) v(t)

>>ode1= diff(u)==u^2/v - u

>>ode2= diff(v) == u^2-v

>>odes=[ode1;ode2]

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Star Strider 2017-6-1

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An analytic (symbolic) solution does not exist. You must us a numeric solver.

The Code —

syms T t u(t) v(t) u0 v0 Y 
Du = diff(u);
Dv = diff(v);
ode1 = Du == u^2/v - u;
ode2 = Dv == u^2-v;
[ode_vf, ode_subs] = odeToVectorField(ode1,ode2);
ode_fcn = matlabFunction(ode_vf, 'vars',{T,Y});
tspan = linspace(0, 10, 150);
icv = [0; 0]+sqrt(eps);
[t,y] = ode45(ode_fcn, tspan, icv);
figure(1)
plot(t, y)
grid

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Walter Roberson 2017-6-2

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Making the assumption that you made a minor typing mistake in entering your question, and that you are asking about

syms u(t) v(t)
ode1= diff(u)==u^2/v - u;
ode2= diff(v) == u^2-v;
odes = [ode1;ode2];
dsolve(odes)

then MATLAB is not able to provide analytic solutions. However, two analytic solutions exist:

u(t) = 0
v(t) = C1 * exp(-t)

where C1 is an arbitrary constant whose value depends upon the initial conditions

u(t) = RootOf(-Intat(-LambertW(-C1*exp(a_)/a_)/(a_*(LambertW(-C1*exp(a_)/a_)+1)), a_ = Z_) + t + C2)
v(t) = u(t)^2/(diff(u(t), t)+u(t))}

that ugly formula for u(t) says that there is a particular function involving a ratio of LambertW formulas, and that for any given t, u(t) is the value such that the integral of the ratio, evaluate at that value, is 0.

This is ugly. But it does provide a path to an analytic solution, of sorts. But it is beyond the capacity of MATLAB.