13.18 problem 20.1 (r)

Internal problem ID [13660]

Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section: Chapter 20. Euler equations. Additional exercises page 382
Problem number: 20.1 (r).
ODE order: 2.
ODE degree: 1.

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

\[ \boxed {3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y=0} \]

Solution by Maple

Time used: 0.0 (sec). Leaf size: 15

dsolve(3*x^2*diff(y(x),x$2)-7*x*diff(y(x),x)+3*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} x^{\frac {1}{3}}+c_{2} x^{3} \]

Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 20

DSolve[3*x^2*y''[x]-7*x*y'[x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^3+c_1 \sqrt [3]{x} \]