Solving and plotting 2nd order ODE

Question

Nina 2023-4-16

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1947893-solving-and-plotting-2nd-order-ode

编辑： Piotr Balik 2023-4-20

I'm trying to solve the equation y''+sin(y)=0, and plot the results at time 0, 0.1, 0.7, 1.5, 3.0, on a graph.

I tried using this code so far to find the solution, but I am unable to plot the result, '2*atan(exp(C1-t)). I think it's because of the 'C1' in the solution, but I'm not sure how to get rid of it.

>> syms y(t)
>> ode = diff(y,t) == -sin(y)
 
ode(t) =
 
diff(y(t), t) == -sin(y(t))
 
>> ySol(t) = dsolve(ode)
 
ySol(t) =
 
2*atan(exp(C1 - t))
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Answer 1

Piotr Balik 2023-4-20

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1947893-solving-and-plotting-2nd-order-ode#answer_1219968

编辑：Piotr Balik 2023-4-20

在 MATLAB Online 中打开

This is constant, whose numerical value is depending on initial conditions.

You can either specify it directly, per Solve system of differential equations - MATLAB dsolve (mathworks.com)

bnds = y(0) == -0.123
ySol(t) = dsolve(ode, bnds)

But you can also try to solve it substituting to general solution analytically:

Plotting and the example code

syms y(t)
ode = diff(y,t) == -sin(y)
bnds = y(0) == -0.123
ySol(t) = dsolve(ode,bnds)
tv = [0, 0.1, 0.7, 1.5, 3.0];
yv = ySol(tv)
figure,
plot(tv,yv,'o-')