50.1.15 problem 2(a)

Internal problem ID [7787]
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)
Date solved : Monday, January 27, 2025 at 03:23:14 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&={\mathrm e}^{3 x}-x \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(diff(y(x),x)=exp(3*x)-x,y(x), singsol=all)
 

\[ y = -\frac {x^{2}}{2}+\frac {{\mathrm e}^{3 x}}{3}+c_{1} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 24

DSolve[D[y[x],x]==Exp[3*x]-x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {x^2}{2}+\frac {e^{3 x}}{3}+c_1 \]