Internal problem ID [10955]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev.
Second edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.2-4 Equation of form
\(x^2 y''+f(x)y'+g(x)y=0\)
Problem number: 121.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+\left (a \,x^{3 n}+b \,x^{2 n}+\frac {1}{4}-\frac {n^{2}}{4}\right ) y=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 104
dsolve(x^2*diff(y(x),x$2)+(a*x^(3*n)+b*x^(2*n)+1/4-1/4*n^2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{-\frac {n}{2}+\frac {1}{2}} \operatorname {hypergeom}\left (\left [\right ], \left [\frac {2}{3}\right ], -\frac {\left (a \,x^{n}+b \right )^{3}}{9 a^{2} n^{2}}\right )+c_{2} \operatorname {hypergeom}\left (\left [\right ], \left [\frac {4}{3}\right ], \frac {-x^{3 n} a^{3}-3 x^{2 n} a^{2} b -3 x^{n} a \,b^{2}-b^{3}}{9 n^{2} a^{2}}\right ) \left (a \,x^{\frac {n}{2}+\frac {1}{2}}+b \,x^{-\frac {n}{2}+\frac {1}{2}}\right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x^2*y''[x]+(a*x^(3*n)+b*x^(2*n)+1/4-1/4*n^2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved