Internal problem ID [5669]
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(d) solving using series.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {y}{x}-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 15
dsolve(diff(y(x),x)+(1/x)*y(x)=x,y(x), singsol=all)
\[ y \relax (x ) = \frac {\frac {x^{3}}{3}+c_{1}}{x} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 19
DSolve[y'[x]+1/x*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2}{3}+\frac {c_1}{x} \\ \end{align*}