Internal problem ID [5667]
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 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^{2}=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
Order:=8; dsolve(diff(y(x),x)-(1/x)*y(x)=x^2,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x \left (1+\mathrm {O}\left (x^{8}\right )\right )+x^{3} \left (\frac {1}{2}+\mathrm {O}\left (x^{5}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 15
AsymptoticDSolveValue[y'[x]-1/x*y[x]==x^2,y[x],{x,0,7}]
\[ y(x)\to \frac {x^3}{2}+c_1 x \]