1.14 problem Problem 1.11(b)

Internal problem ID [12407]

Book: Differential Equations, Linear, Nonlinear, Ordinary, Partial. A.C. King, J.Billingham, S.R.Otto. Cambridge Univ. Press 2003
Section: Chapter 1 VARIABLE COEFFICIENT, SECOND ORDER DIFFERENTIAL EQUATIONS. Problems page 28
Problem number: Problem 1.11(b).
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]

\[ \boxed {y^{\prime \prime } x^{2}+y^{\prime }-2 y=0} \] With the expansion point for the power series method at \(x = 0\).

✗ Solution by Maple

Order:=6; 
dsolve(x^2*diff(y(x),x$2)+diff(y(x),x)-2*y(x)=0,y(x),type='series',x=0);
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 28

AsymptoticDSolveValue[x^2*y''[x]+y'[x]-2*y[x]==0,y[x],{x,0,5}]
                                                                                    
                                                                                    
 

\[ y(x)\to c_2 e^{\frac {1}{x}} x^2+c_1 \left (2 x^2+2 x+1\right ) \]