1.10 problem Problem 16

Internal problem ID [2087]

Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section: Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number: Problem 16.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_Emden, _Fowler]]

Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 25

dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+13*y(x)=0,y(x), singsol=all)
 

\[ y \relax (x ) = c_{1} x^{2} \sin \left (3 \ln \relax (x )\right )+c_{2} x^{2} \cos \left (3 \ln \relax (x )\right ) \]

Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 26

DSolve[x^2*y''[x]-3*x*y'[x]+13*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x^2 (c_2 \cos (3 \log (x))+c_1 \sin (3 \log (x))) \\ \end{align*}