How to solve 2nd ODE equation in numerical and analytical method at same plot graph?

2022 9 28
1 个回答
更新时间：2022 10 12
5 次查看（30 天）

0 个投票

Hello,
I am was looking for help to solve this equation
a. dx/dt = -x
b. dx/dt = -x+1
in Matlab, can I get help to solve this equation of plot the numerical solutions and analytical solutions in the same graph and compare them.
with ode45
can anyone help me with this code?

6 个评论
显示 4更早的评论 隐藏 4更早的评论

Shreyas Sangamesh
Shreyas Sangamesh 2022-9-28
移动：Star Strider 2022-9-28
I was looking for these kind of equation as well, by the way 2nd ODE solution was very helpful.
can you help me in these kind of equation as well?
majorly for the dsolve part.
Star Strider
Star Strider 2022-9-28
移动：Star Strider 2022-9-28
Just substitute each of those equations into ‘DEqn’ in my previous code, and go from there with each one separately. Make appropriate changes in the initial conditions and time limits as necessary (since I guessed at those).
John D'Errico
John D'Errico 2022-9-28
PLease stop asking the same question every 30 minutes. You asked this question before, and got an answer.
Shreyas Sangamesh
Shreyas Sangamesh 2022-9-28
Its not the same one I asked before,
I just wanted to have some assistance on how these equation behave in 1st order ODE,
I have got the revelant idea on how to carry it out!!
Thank you
Torsten
Torsten 2022-9-28
编辑：Torsten 2022-9-28
a .
dx/dt = - x -> dx/x = -dt -> log(x/x0) = (t0-t) -> x = x0 * exp(t0-t)
b.
dx/dt = -x+1 -> dx/(x-1) = -dt -> log((x-1)/(x0-1)) = t0-t -> x-1 = (x0-1)*exp(t0-t) -> x = 1 + (x0-1)*exp(t0-t)

请先登录，再进行评论。

请先登录，再回答此问题。

回答（1 个）

Sai
Sai 2022-10-12

0 个投票

I understand that you are trying to solve the differential equations both numerically and analytically and get the plots on same graph for comparison.
You can use available MATLAB functions “ode45” for numerical approach and “dsolve” for analytical approach.
Please refer to the attached code snippets, which can help you solve the problem.
NOTE: Since the initial conditions are not given, they are assumed
a). dx/dt = -x
%Numerical Method
[t,x] = ode45(@(t,x) -x,[0 20],1)
plot(t,x)
hold on
%Analytical Method
syms x(t)
dx = diff(x)
eqn = dx==-x
x(t) = dsolve(eqn,x(0)==1)
t = 0:20
plot(t,x(t))
hold off
legend("Numerical","Analytical")
b). dx/dt = -x+1
%Numerical Method
[t,x] = ode45(@(t,x) -x+1,[0 20],0)
plot(t,x)
hold on
%Analytical Method
syms x(t)
dx = diff(x)
eqn = dx==-x+1
x(t) = dsolve(eqn,x(0)==0)
t = 0:20
plot(t,x(t))
hold off
legend("Numerical","Analytical")
You can also refer to the below links regarding “ode45” and “dsolve” for future references.

类别

在 帮助中心 和 File Exchange 中查找有关 Ordinary Differential Equations 的更多信息

标签

回答：

Sai
Sai
2022-10-12

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by