Internal problem ID [5543]
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(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {4 x^{2} y^{\prime \prime }-3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 15
dsolve(4*x^2*diff(y(x),x$2)-3*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = x^{\frac {3}{2}} c_{1}+\frac {c_{2}}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 20
DSolve[4*x^2*y''[x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_2 x^2+c_1}{\sqrt {x}} \\ \end{align*}