Internal problem ID [5540]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.1. Linear Equations with Constant
Coefficients. Page 62
Problem number: 5(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+3 x y^{\prime }+10 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)+10*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \sin \left (3 \ln \relax (x )\right )}{x}+\frac {c_{2} \cos \left (3 \ln \relax (x )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 26
DSolve[x^2*y''[x]+3*x*y'[x]+10*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 \cos (3 \log (x))+c_1 \sin (3 \log (x))}{x} \\ \end{align*}