Change of dependent variable

A change of dependent variable expresses the unknown function of a differential equation in terms of a new unknown, while keeping the independent variable fixed. For example, substituting $y=e^{-ax/2}v$ in $y^{\prime \prime }+a{y}^{\prime }+by=f$ removes the first derivative and gives $v^{\prime \prime }+(b-a^2/4)v=e^{ax/2}f$ when $a,b$ are constant. Transforming the boundary conditions as well is essential, particularly for a Robin boundary condition.