Internal problem ID [6188]
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: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(2*x^2*diff(y(x),x$2)+5*x*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \sqrt {x}\, c_{1}+\frac {c_{2}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 20
DSolve[2*x^2*y''[x]+5*x*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x^{5/2}+c_1}{x^2} \\ \end{align*}