Internal problem ID [4176]
Book: A treatise on ordinary and partial differential equations by William Woolsey Johnson.
1913
Section: Chapter 1, Nature and meaning of a differential equation between two variables. page
12
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-{\mathrm e}^{a x}-y a=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve(diff(y(x),x)=exp(a*x)+a*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (x +c_{1} \right ) {\mathrm e}^{a x} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 15
DSolve[y'[x]==Exp[a*x]+a*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{a x} (x+c_1) \\ \end{align*}