Internal problem ID [2391]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 11, Series Solutions to Linear Differential Equations. Exercises for 11.2. page
739
Problem number: Problem 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y^{\prime } x^{2}-2 y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
Order:=6; dsolve(diff(y(x),x$2)-x^2*diff(y(x),x)-2*x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {x^{3}}{3}\right ) y \relax (0)+\left (x +\frac {1}{4} x^{4}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 28
AsymptoticDSolveValue[y''[x]-x^2*y'[x]-2*x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^4}{4}+x\right )+c_1 \left (\frac {x^3}{3}+1\right ) \]