Internal problem ID [10895]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev.
Second edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.2-3 Equation of form
\((a x + b)y''+f(x)y'+g(x)y=0\)
Problem number: 61.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {x y^{\prime \prime }+\frac {y^{\prime }}{2}+a y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(x*diff(y(x),x$2)+1/2*diff(y(x),x)+a*y(x)=0,y(x), singsol=all)
\[ y = c_{1} \sin \left (2 \sqrt {a}\, \sqrt {x}\right )+c_{2} \cos \left (2 \sqrt {a}\, \sqrt {x}\right ) \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 38
DSolve[x*y''[x]+1/2*y'[x]+a*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \cos \left (2 \sqrt {a} \sqrt {x}\right )+c_2 \sin \left (2 \sqrt {a} \sqrt {x}\right ) \]