[ empty sym ] & "unable to find explicit solution" error when using dsolve for second order differential equation

Question

James Stirling 2020-4-21

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https://ww2.mathworks.cn/matlabcentral/answers/519699-empty-sym-unable-to-find-explicit-solution-error-when-using-dsolve-for-second-order-differen

回答： Jyotsna Talluri 2020-4-24

I'm trying to solve a second order differential equation with 4 variations of one of the initital conditions, but no matter if I try to do all of them at once (the commented d = line) or just one at a time (the d=1) matlab says "Warning: unable to find an explicit solution" and spits out "ySol1 = [ empty sym ]". I don't think there's no solution, as there are a couple follow up questions in the homework problem this is from. What am I doing wrong? Does this equation need ode45 over dsolve, and if so how would I format it?

syms y(t) d;
Dy = diff(y);
% d = [1 1.5 2 2.5];
d = 1;
cond1 = y(0) == d;
cond2 = Dy(0) == 0;
conds = [cond1 cond2];
ySol1 = dsolve(diff(y,t,2)+0.15*Dy-y+y^3 == 0, conds)

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Answer 1

Jyotsna Talluri 2020-4-24

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syms y(t) 
[v] = odeToVectorField(diff(y,t,2)+0.15*diff(y,t)+y-y^3 == 0);
M = matlabFunction(v,'vars', {'t','Y'});
t= [0 20];
cond = [1  0];
sol = ode45(M, t, cond);