MATLAB: How to plot a first order differential equation with singular point

MATLABode45

Is there a way to plot a first or second order differential equation with singular point? Example equation:

(1-y^2)*y" + 5*y' + 3*y = 0

Usually I get error message from ode about division by zero.

Save this file as odef.m

function dx=odef(t,x)
dx=zeros(2,1)
dx(1)=x(2);
dx(2)=(-5*x(2)-3*x(1))/(1-x(1)^2)

Then call it

%y'(0)=0.1 and y(0)=0.1  are initial conditions
tspan=[0 10]
[t,y]=ode45(@odef,tspan,[0.1 ;0.1])
plot(t,y)

Main program

y0=[0 1];
tspan=[0 10];
[t,y]=ode45(@myeq,tspan,y0)

save this function as myeq.m

function dx=myeq(t,x)
dx=zeros(2,1);
dx(1)=x(1)-x(1)^3+x(2); 
dx(2)=3*x(1)-x(2) ;

You can transform your equation d2y/dx2=.-5dy/dx-7y to get:

y1=y
y2=dy/dx
dy1=dy/dx=y2
dy2=d2y/d2x=-5dy/dx-7y=-5y2-7y1

Create a file named myode.m

function dy=myode(x,y)
dy=[0;0]
dy(1)=y(2)
dy(2)=-5*y(2)-7*y(1)

Then run these lines

yin=[0 4 ]  % initial values
time=[0 5]
[x,y]=ode45(@myode,time,yin)
plot(x,y)