Internal problem ID [13656]
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 (n).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {4 x^{2} y^{\prime \prime }+37 y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve(4*x^2*diff(y(x),x$2)+37*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {x}\, \left (c_{1} \sin \left (3 \ln \left (x \right )\right )+c_{2} \cos \left (3 \ln \left (x \right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 28
DSolve[4*x^2*y''[x]+37*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {x} (c_2 \cos (3 \log (x))+c_1 \sin (3 \log (x))) \]