Internal problem ID [10948]
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: 114.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-\left (a^{2} x^{2}+2 b a x +b^{2}-b \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(x^2*diff(y(x),x$2)-(a^2*x^2+2*a*b*x+b^2-b)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{b} {\mathrm e}^{a x}+c_{2} \operatorname {WhittakerM}\left (-b , -b +\frac {1}{2}, 2 a x \right ) \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 38
DSolve[x^2*y''[x]-(a^2*x^2+2*a*b*x+b^2-b)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 M_{-b,b-\frac {1}{2}}(2 a x)+c_2 W_{-b,b-\frac {1}{2}}(2 a x) \]