34.1.5 problem 5

Internal problem ID [6029]
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
Date solved : Monday, January 27, 2025 at 01:33:40 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&={\mathrm e}^{a x}+a y \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

dsolve(diff(y(x),x)=exp(a*x)+a*y(x),y(x), singsol=all)
 

\[ y = \left (x +c_1 \right ) {\mathrm e}^{a x} \]

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 15

DSolve[D[y[x],x]==Exp[a*x]+a*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{a x} (x+c_1) \]