Internal problem ID [210]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.3, second order linear equations. Page 323
Problem number: 52.
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 }+y^{\prime } x +9 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+9*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (3 \ln \relax (x )\right )+c_{2} \cos \left (3 \ln \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 22
DSolve[x^2*y''[x]+x*y'[x]+9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cos (3 \log (x))+c_2 \sin (3 \log (x)) \\ \end{align*}