SOLVED:The reduction of order procedure can be used more generally to reduce a homogeneous linear n th-order equation to a homogeneous linear (n-1) th-order equation. For the equation t y^'''-t y^'' y^'-y=0 which has f(t)=e^t as a solution, use the substitution y(t)=v(t) f(t) to reduce this third-order equation to a homogeneous linear second-order equation in the variable w=v^'.

4.6: Reduction of Order

How to Build Reduced Order Models of CFD Simulations | Ansys