50.17.18 problem 2(c) solving directly

Internal problem ID [8089]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 4. Power Series Solutions and Special Functions. Section 4.2. Series Solutions of First-Order Differential Equations Page 162
Problem number : 2(c) solving directly
Date solved : Monday, January 27, 2025 at 03:43:31 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

dsolve(diff(y(x),x)-(1/x)*y(x)=x^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 17

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

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