Solve second order differential equation with independent variable

I need the solution to the following second order differential equation:

D2y+(2/x)*Dy= 10*(y/(1+y));

I want to use ode45 for this. I have split the equation in the following manner :

%y(1)=y(x);

%y(2)=Y'(x);

So the equation can be written as :

y'(1)=y(2);

y'(2)=10*(Y(1)/(1+(y(1)))-(2/x)*Y(2);

When I solve this usind ode45, I get a matrix comprising of Nan values.

I believe the variation of the independent variable, i.e x, cannot be done like this.

I am not sure how to solve this.

Any help would be appreciated. Thanks! :)

[Amit]

Post the code for your function? Also what are the initial values for Y and Y'

[Abhivyakti]

I just know one condition here, i.e When x is 'R', y id 's0'. Here R,s0 are constants.

Answer 1

[Azzi Abdelmalek]

Your function should be:

function dz=myode45(x,z)
dz(1,1)=z(2)
dz(2,1)=-2*z(2)/x+10*z(1)/(z(1)+1)

%Call myode45

tspan=[0.1 10]; 
% don't start tspan at 0, because in your equation there is -2z(2)/x
y0=[0;1]; % initial conditions  
[x,y]=ode45('myode45',tspan,y0)

[Abhivyakti]

This works but I have a doubt.

The only condition to be followed here is that, when x=R, y=s0.

Both R and s0 are constants predefined.

So how do I incorporate this condition into the program above.

[Azzi Abdelmalek]

Your differential equation contains two states y and dy, you have to set their initial conditions

[Abhivyakti]

Alright. Tell me one thing, is it that 'tspan' is supposed to incorporate the variation of the values of 'x' ? I understood the values 'y' is storing but what about 'x' and 'tspan' ?

[Azzi Abdelmalek]

tspan=[t0 tf] % t0 is a start time, and tf is a final time
x represent time or whatever you want. It's in your equation