3.3.14 First order special form ID 1 $y^{\prime }=g\left(x\right)e^{a\left(x\right)+by}+f\left(x\right)$

ode internal name "first order special form ID 1"

This is special form which did not fit in any of the above ones. Solved by the substitution $u=e^{-by}$ which converts the ode to a linear first order ode in $u\left(x\right)$ which is solved, then $y$ is found. $b$ must not depend on $x$ for this to work.