50.3.11 problem 2(a)

Internal problem ID [7835]
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 : 2(a)
Date solved : Monday, January 27, 2025 at 03:24:26 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 15

dsolve([diff(y(x),x)-x*y(x)=0,y(1) = 3],y(x), singsol=all)
 

\[ y = 3 \,{\mathrm e}^{\frac {\left (x -1\right ) \left (x +1\right )}{2}} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 18

DSolve[{D[y[x],x]-x*y[x]==0,{y[1]==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 e^{\frac {1}{2} \left (x^2-1\right )} \]