Internal problem ID [5366]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS.
Page 9
Problem number: 2(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{3 x}+x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 17
dsolve(diff(y(x),x)=exp(3*x)-x,y(x), singsol=all)
\[ y \relax (x ) = -\frac {x^{2}}{2}+\frac {{\mathrm e}^{3 x}}{3}+c_{1} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 24
DSolve[y'[x]==Exp[3*x]-x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^2}{2}+\frac {e^{3 x}}{3}+c_1 \\ \end{align*}