Internal problem ID [5690]
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 4.4. REGULAR SINGULAR
POINTS. Page 175
Problem number: 1(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime }=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✗ Solution by Maple
Order:=8; dsolve(x^2*diff(y(x),x$2)+(2-x)*diff(y(x),x)=0,y(x),type='series',x=0);
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 64
AsymptoticDSolveValue[x^2*y''[x]+(2-x)*y'[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 e^{2/x} \left (\frac {2835 x^7}{2}+315 x^6+\frac {315 x^5}{4}+\frac {45 x^4}{2}+\frac {15 x^3}{2}+3 x^2+\frac {3 x}{2}+1\right ) x^3+c_1 \]