Internal problem ID [6181]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 18. Power series solutions. 18.4 Indicial Equation with Difference of Roots
Nonintegral. Exercises page 365
Problem number: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {2 x^{2} y^{\prime \prime }+x y^{\prime }-y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.024 (sec). Leaf size: 25
Order:=8; dsolve(2*x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {x^{\frac {3}{2}} c_{2}+c_{1}}{\sqrt {x}}+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 16
AsymptoticDSolveValue[2*x^2*y''[x]+x*y'[x]-y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 x+\frac {c_2}{\sqrt {x}} \]