title: Can I run ode45 backwards in time?
body: <p>I use ode45 to solve differential equations but the tspan always has to be such that the system runs forward in time. Can I make ode45 run the system backwards to negative t? </p>
  
  <p>The specific problem I have uses a rising exponential function i.e a*exp(at) from t=-infinity to t=0 and the function is zero for all t>0. As you can see, it isn't possibly to translate this function and use the interval t=0 to t=infinity in my problems. So, I would like ode45 to work in negative t. </p>
  
  <p>Thank you!</p>
  
  <p>EDIT: After some thinking, I realize that my question is phrased badly and I had a poor understanding too so let me restate it here. </p>
  
  <p>My ODEs are of the form x'=f(t)x, where f(t)=a*exp(at) from -infinity to 0. The system starts with some intial conditions at t=-infinity. ode45 on the other hand requires tspan to be positive and also requires the initial conditions at t=0. So how can I change both these criteria? </p>
  
  <p>Thank you :) </p>