Internal problem ID [4340]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page
435
Problem number: 16 (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 y^{\prime } x -3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x^{3}}+c_{2} x \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 16
DSolve[x^2*y''[x]+3*x*y'[x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1}{x^3}+c_2 x \\ \end{align*}