Here we use Matlab to numerically solve a simple ordinary differential equation:

$x+x=0$

$x(0)=0\mathrm{.}1$

As a first step, we re$-$wnite this equation as:

hat$(x)=-x$

Wc use ODE$45$ function to solve this ODE. To use ODE$45,$ you need two Matlab functions. The first one defines your equation. I have called this ofe$\_$function$\_$fiest$\_$order:

$dydt=(-y(1))$

end

The second one calls ODE$45$ to solve the equation that you have defined. I have called this obs $1$st order

What

tepan$=(0101)$

yo $=10\mathrm{.}11$

plot $(t,y($:$,1))$

The last line in the function plots the results.

I have uploaded these two functions as two scparate files. Make a new folder in your computer, Copy both of these files in the same folder. Open Matlab. Go to that directory. Type

ODE$\_1$st Order

and enter.

You should be looking at the solution of that equation.

Now solve the following problem:

$x-xcosx-1=0$

$x(0)=0\mathrm{.}05$