2:Second and higher order ODEs with initial conditions Initial value problems (IVPS) The higher order ODE with initial conditions can be converted into the system of first order ODEs of the types For example y"+xy' + y = sin(x); y(0)=1, y'(0)=1 Let y'=z, using this in above equation, we have 2'+xz+ y = sin(x) (or) z' = sin(x)-xz-y