ODE analytical solution

How can I find the analytical solution to the following ode?

    y'+ x/y=0
 when x=0 and y=5.

Answer 1

[bym]

simplify(dsolve('Dy=-x/y','y(0)=5','x'))

ans =

(25 - x^2)^(1/2)

[John]

From my text book I have coded Euler's Method to solve ODEs but i am confused on where to input each into the program the code I have is

function [t,y] = eulode(dydt, tspan, y0, h)

%eulode: Euler ODE solver

% [t,y] = eulode(dydt, tspan, y0, h, p1, p2,...)

% ` uses EULER'S method to INTEGRATE an ODE

% (uses the slope at the beginning of the stepsize to graph the

% function.)

%Input:

% dydt = name of hte M-file that evaluates the ODE

% tspan = [ti,tf] where ti and tf = initial and final values of

% independent variables

% y0 = initial value of dependent variable

% h = step size

% p1,p2 = additional parameter used by dydt

%Output:

% t = vector of independent variable

% y = vector of solution for dependent variable

if nargin<4, error('at least 4 input arguments required'), end

ti = tspan(1); tf = tspan(2);

if ~ (tf>ti), error('upper limit must be greater than lower limit'), end

t = (ti:h:tf)';

n = length(t);

%if necessary, add an additional value of t

%so that range goes from t=ti to tf

if t(n)<tf

t(n+1) = tf;

n = n+1;

t(n)=tf;

end

y = y0*ones(n,1); %preallocate y to improve efficiency

for i = 1:n-1 %implement Euler's Method

y(i+1) = y(i) + dydt(t(i),y(i))*(t(i+1)-t(i));

end

plot(t,y)

in my other m-file I am supposed to run the program with 3 different step sizes (.5; .1; .01) so my code looks like this

dydx=@(x,y) -(x/y);

[x1,y1]=eulode(dydx, [0 1],5,.5);

[x2,y2]=eulode(dydx,[0 1],5,.1);

[x3,y3]=eulode(dydx,[0 1],5,.01);

disp([x1,y1])

disp([x2,y2])

disp([x3,y3])

I think this is correct because each answer is displaying a value close to 5 (which the analytical value should be 5 since x=0)

Did i code this right?