How find symbolic solution matlab

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Juan Saa 2020-11-23

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评论： Juan Saa 2020-11-23

I am trying to solve this simple autonomous differential equation using the dsolve function but MATLAB cannot find a symbolic solution to the function. Does anyone have any idea how I could solve the problem? The code is the following:

clc, clear all
syms y(t) 
eqn = diff(y,t,2) == -9.8*sin(y) - 0.5*y'
Dy = diff(y,t)
cond = [y(0)==0.8, Dy(0)==0.8]
ySol(t) = dsolve(eqn,cond)

Thanks in advance to anyone who can help me.

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John D'Errico 2020-11-23

It cannot find a symbolic solution because one apparently does not exist. And that is why Stephan was asking if you really intended sin(t), not sin(y), as there may well be a solution in that case.

Juan Saa 2020-11-23

I understand, thanks for your help

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回答（1 个）

Stephan 2020-11-23

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It appears that there either is no symbolic solution or Matlab is not powerful enough to find one. For sin(t) it would work. However Wolfram Alpha also does not provide an analytical solution for this ode - here is the numeric approach:

syms y(t) 
Dy = diff(y,t)
eqn = diff(y,t,2) == -9.8*sin(y) - 0.5*Dy
% make numeric function from symbolic
[V,S] = odeToVectorField(eqn)
fun = matlabFunction(V,'Vars',{'t','Y'})
% solve ode numeric
[t,y] = ode45(fun,[0 10],[0.8, 0.8]);
plot(t,y)