MATLAB: Y”-y’ y=sin(x) +exp(x)

from me

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

Best Answer

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.

Related Solutions

MATLAB: Solve differential equation using ode23 and ode45

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

MATLAB: How to solve y”+y’-2y=x

Something like this perhaps:

Y0 = [2 5];    % intial conditions
xspan = [0 5];  % x-boundary values
% ode solver
[x, Y] = ode45(@rates, xspan, Y0);
% note that Y(:,1) are the y values and Y(:,2) are the y' values
% Plot results
plot(x, Y)   
function dYdx = rates(x,Y)
         y = Y(1);
         v = Y(2);
         dydx = v;
         dvdx = -v + 2*y +x.^2 + x;
         dYdx = [dydx; dvdx];
end

Best Answer

Related Solutions

MATLAB: Solve differential equation using ode23 and ode45

MATLAB: How to solve y”+y’-2y=x

Related Question