75.24.9 problem 749

Internal problem ID [17221]
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 ODEs). Section 18.2. Expanding a solution in generalized power series. Bessels equation. Exercises page 177
Problem number : 749
Date solved : Tuesday, January 28, 2025 at 09:57:54 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{4}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (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*D[y[x],{x,2}]+1/2*D[y[x],x]+1/4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cos \left (\sqrt {x}\right )+c_2 \sin \left (\sqrt {x}\right ) \]