Internal problem ID [5668]
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.
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*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 13
dsolve(diff(y(x),x)-(1/x)*y(x)=x^2,y(x), singsol=all)
\[ y \relax (x ) = \left (\frac {x^{2}}{2}+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 17
DSolve[y'[x]-1/x*y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^3}{2}+c_1 x \\ \end{align*}