title: Derivative of y^3 using Matlab ode45
body: <p>I have two differential equations I would like to solve simultaneously using ode45 in Matlab, shown below.
  The problem I have is that the second differential equation is actually d(y^3)/dt, i.e. the derivative of y^3 with respect to t. How do I express this?</p>
  
  <pre><code>function dydt=odefcnNY(t,y,D,Cs,rho,r0,Af,N,V)
  dydt=zeros(2,1);
  dydt(1)=(3*D*Cs/rho*r0^2)*(y(1)/r0)*(1-y(2)/Cs);
  dydt(2)=(D*4*pi*r0*N*(1-y(2)/Cs)*(y(1)/r0)-(Af*y(2)/Cs))/V;
  end
  
  D=4e-9;
  rho=1300;
  r0=10.1e-6;
  Cs=0.0016;
  V=1.5e-6;
  W=4.5e-8;
  N=W/(4/3*pi*r0^3*rho);
  Af=0.7e-6/60;
  tspan=[0 75000];
  y0=[r0 Cs];
  [t,y]=ode45(@(t,y) odefcnNY(t,y,D,Cs,rho,r0,Af,N,V), tspan, y0);
  plot(t,y(:,1),'-o',t,y(:,2),'-.')
  </code></pre>