50.3.14 problem 2(d)

Internal problem ID [7838]
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(d)
Date solved : Monday, January 27, 2025 at 03:24:28 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {y}{x}&=x^{2} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 12

dsolve([diff(y(x),x)-y(x)/x=x^2,y(1) = 3],y(x), singsol=all)
 

\[ y = \frac {\left (x^{2}+5\right ) x}{2} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 15

DSolve[{D[y[x],x]-y[x]/x==x^2,{y[1]==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} x \left (x^2+5\right ) \]