Internal problem ID [2227]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.1, General Theory for Linear
Differential Equations. page 502
Problem number: Problem 34.
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 {x^{2} y^{\prime \prime }+3 y^{\prime } x -8 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 15
dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)-8*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x^{4}}+x^{2} c_{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 18
DSolve[x^2*y''[x]+3*x*y'[x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x^6+c_1}{x^4} \\ \end{align*}