y''-y' y=sin(x) +exp(x)

I do not know how to solve it if I do not use dsolve

[John D'Errico]

doc ode45

You might even see an example there that will explain how to solve a second order ODE.

[thang phung]

thank you, let me try

[Star Strider]

Two Symbolic Math Toolbox functions you will find useful are odeToVectorField and matlabFunction.

[thang phung]

[thang phung]

why they're so different ?

Answer 1

[Star Strider]

They are different because odeToVectorField gives you an array you can pass to matlabFunction that will give you an anonymous function you can use directly with ode45 (if you write the matlabFunction call correctly), to get a numeric solution.

The result of your dsolve call gives you the analytic solution to the differential equation.

They are two entirely different results.

[thang phung]

If I want to find out the same result as the result of dsolve but I do not want to use dsolve but the other method. Could you show me that method, please?

[Star Strider]

I will get you started:

syms y(t) Y T 
[YDE,Subs] = odeToVectorField(diff(y,2) - 2*diff(y) + y == sin(t) + exp(t));
ode_fcn = matlabFunction(YDE, 'Vars',{t,Y});

You can use ‘ode_fcn’ directly with ode45.

I also requested the ‘Subs’ output from odeToVectorField so you will know that the first row (and first column of the result returned by ode45) is ‘y’, and the second of both is ‘Dy’.

[thang phung]

thank you so much

[Star Strider]

As always, my pleasure.