Internal problem ID [6421]
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]
\[ \boxed {y^{\prime }-\frac {y}{x}=x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(x),x)-(1/x)*y(x)=x^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x \left (x^{2}+2 c_{1} \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 17
DSolve[y'[x]-1/x*y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^3}{2}+c_1 x \]