60.3.126 problem 1130

Internal problem ID [11136]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1130
Date solved : Monday, January 27, 2025 at 10:46:40 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 31

dsolve(2*x*diff(diff(y(x),x),x)+diff(y(x),x)+a*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \sin \left (\sqrt {x}\, \sqrt {2}\, \sqrt {a}\right )+c_{2} \cos \left (\sqrt {x}\, \sqrt {2}\, \sqrt {a}\right ) \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 46

DSolve[a*y[x] + D[y[x],x] + 2*x*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cos \left (\sqrt {2} \sqrt {a} \sqrt {x}\right )+c_2 \sin \left (\sqrt {2} \sqrt {a} \sqrt {x}\right ) \]