Internal problem ID [15491]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 18.2. Expanding a solution in generalized power
series. Bessels equation. Exercises page 177
Problem number: 749.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {y^{\prime \prime } x +\frac {y^{\prime }}{2}+\frac {y}{4}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x*diff(y(x),x$2)+1/2*diff(y(x),x)+1/4*y(x)=0,y(x), singsol=all)
\[ y = c_{1} \sin \left (\sqrt {x}\right )+c_{2} \cos \left (\sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 24
DSolve[x*y''[x]+1/2*y'[x]+1/4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \cos \left (\sqrt {x}\right )+c_2 \sin \left (\sqrt {x}\right ) \]