3.14 problem 2(d)

Internal problem ID [5417]

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).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime }-\frac {y}{x}-x^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 3] \end {align*}

Solution by Maple

Time used: 0.032 (sec). Leaf size: 12

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

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

Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 15

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

\begin{align*} y(x)\to \frac {1}{2} x \left (x^2+5\right ) \\ \end{align*}