Internal problem ID [13490]
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: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }+\frac {5 y}{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(x^2*diff(y(x),x$2)+5/2*y(x)=0,y(x), singsol=all)
\[ y = c_{1} \sqrt {x}\, \sin \left (\frac {3 \ln \left (x \right )}{2}\right )+c_{2} \sqrt {x}\, \cos \left (\frac {3 \ln \left (x \right )}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 32
DSolve[x^2*y''[x]+5/2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {x} \left (c_2 \cos \left (\frac {3 \log (x)}{2}\right )+c_1 \sin \left (\frac {3 \log (x)}{2}\right )\right ) \]