Solving 2nd Order Differential Equation Symbolically

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Jordan Stanley
Jordan Stanley 2022-4-15
评论： Walter Roberson 2024-9-19
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 =
Error using eval
Unrecognized function or variable 'C1'.
I'd greatly appreciate any assistance.

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采纳的回答

Star Strider
Star Strider 2022-4-15
Ran in:
The constants are the initial condition. They must be defined.
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])
ySol(x, 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 个评论
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Torsten
Torsten 2022-4-16
编辑：Torsten 2022-4-16
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 ?
Jordan Stanley
Jordan Stanley 2022-4-16
编辑：Jordan Stanley 2022-4-16
Well I should mention that we were supposed to choose a 2nd order differential eqaution initial value problem from our textbook and maybe I just happened to choose a more complicated eqaution to use.
Ok, well interestingly enough upon running the code agin that Star Strider suggested I did not get an error message this time.

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更多回答（1 个）

jatin
jatin 2024-9-19
clear all;
clc;
close all;
num = [0 10];
den= [0 0];
[t, y] = ode45(@ode_system,num,den)]
plot(t, y(:,1));
xlabel('Time t');
ylabel('Solution y(t)');
title('Solution of the second-order differential equation');
grid on;
end

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