Internal problem ID [13823]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 25. Review exercises for part III. page 447
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(9*x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} +c_{2} \ln \left (x \right )\right ) x^{\frac {1}{3}} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 24
DSolve[9*x^2*y''[x]+3*x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} \sqrt [3]{x} (c_2 \log (x)+3 c_1) \]