50.3.1 problem 1(a)

Internal problem ID [7825]
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 1.4 First Order Linear Equations. Page 15
Problem number : 1(a)
Date solved : Monday, January 27, 2025 at 03:24:20 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }-y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 12

dsolve(diff(y(x),x)-x*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 22

DSolve[D[y[x],x]-x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{\frac {x^2}{2}} \\ y(x)\to 0 \\ \end{align*}