Solve differential equation using ode23 and ode45

Question

emonhossain roy 2019-6-24

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https://ww2.mathworks.cn/matlabcentral/answers/468671-solve-differential-equation-using-ode23-and-ode45

评论： Pullak Barik 2019-6-25

Question: solve the differential equation

regarding y as the independent variable rather than x. Also find solution for x(0)=1. Finally plot y vs x(y). Also use ode23 and ode45 to solve the equation and plot again.

My approach:

code:

syms x(y);

eqn=diff(y,x)==(x+y*exp(y));

cond=x(0)==1;

dsolve(eqn,cond)

But now how to use ode23 or ode45 and how to plot? Any solution will be appreciated .

Thanks in advance .

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emonhossain roy 2019-6-24

@Star Strider I edited my post

Torsten 2019-6-25

编辑：Torsten 2019-6-25

No, you didn't since you still write

eqn=diff(y,x)==(x+y*exp(y));

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Answer 1

Pullak Barik 2019-6-25

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https://ww2.mathworks.cn/matlabcentral/answers/468671-solve-differential-equation-using-ode23-and-ode45#answer_380677

在 MATLAB Online 中打开

Firstly, as correctly mentioned in the comments, the eqn variable should be written as-

eqn = diff(x, y) == (x + y*exp(y));

Now, for plotting the solution, you can use fplot- fplot documentation

xSol = simplify(dsolve(eqn, cond)); %simplify, as the name suggests, simplifies the expression obtained after dsolve
fplot(xSol);

Now, about using ode23 or ode45, I suggest you to refer to the documentation to gain an understanding on the same. I am posting a code below which uses ode45 (referred directly from the documentation)-

[y, x] = ode45(@(y, x) (x + y*exp(y)), [-10 10], 1)

Link to ode45 documentation- ODE45