![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/965510/image.png)
Solving 2nd Order Differential Equation Symbolically
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Jordan Stanley
on 15 Apr 2022
Edited: Jordan Stanley
on 16 Apr 2022
Hello,
I have the 2nd order differential equation: y'' + 2y' + y = 0 with the initial conditions y(-1) = 0, y'(0) = 0.
I need to solve this equation symbolically and graph the solution.
Here is what I have so far...
syms y(x)
Dy = diff(y);
D2y = diff(y,2);
ode = D2y + 2*Dy + y == 0;
ySol = dsolve(ode,[y(-1)==0,Dy(0)==0])
a = linspace(0,1,20);
b = eval(vectorize(ySol));
plot(a,b)
But I get the following output.
ySol = ![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/965485/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/965485/image.png)
Error using eval
Unrecognized function or variable 'C1'.
I'd greatly appreciate any assistance.
0 Comments
Accepted Answer
Star Strider
on 15 Apr 2022
The
constants are the initial condition. They must be defined.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/965510/image.png)
syms y(x) y0
Dy = diff(y);
D2y = diff(y,2);
ode = D2y + 2*Dy + y == 0;
ySol(x,y0) = dsolve(ode,[Dy(0)==0,y(-1)==0,y(0)==y0])
% a = linspace(0,1,20);
% b = eval(vectorize(ySol));
figure
fsurf(ySol,[0 1 -1 1])
xlabel('x')
ylabel('y_0 (Initial Condition)')
.
16 Comments
Torsten
on 16 Apr 2022
Edited: Torsten
on 16 Apr 2022
How should it be possible to solve 1. without 2. ? If you don't know the solution, you can't trace a solution curve. Or what's your opinion ?
Anyhow - I think your instructors overlooked that the equation together with its initial conditions does not only give one curve, but infinitly many. So "graphing the solution" will become difficult. But Star Strider's answer for this situation looks fine for me.
But you say you get an error. What's your code and what's the error message ?
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