Internal problem ID [6185]
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: 25.
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*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 13
dsolve(2*x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +\frac {c_{2}}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 18
DSolve[2*x^2*y''[x]+x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1}{\sqrt {x}}+c_2 x \\ \end{align*}