Internal problem ID [11068]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev.
Second edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.2-8. Other equations.
Problem number: 244.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{n} y^{\prime \prime }+\left (a \,x^{n -1}+b x \right ) y^{\prime }+\left (a -1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.782 (sec). Leaf size: 137
dsolve(x^n*diff(y(x),x$2)+(a*x^(n-1)+b*x)*diff(y(x),x)+(a-1)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = x^{-\frac {a}{2}-\frac {1}{2}+\frac {n}{2}} {\mathrm e}^{\frac {b \,x^{2-n}}{-4+2 n}} \left (\operatorname {WhittakerM}\left (\frac {\left (-b +2\right ) a -2+b \left (n -1\right )}{2 b \left (n -2\right )}, \frac {a -1}{-4+2 n}, \frac {b \,x^{2-n}}{n -2}\right ) c_{1} +\operatorname {WhittakerW}\left (\frac {\left (-b +2\right ) a -2+b \left (n -1\right )}{2 b \left (n -2\right )}, \frac {a -1}{-4+2 n}, \frac {b \,x^{2-n}}{n -2}\right ) c_{2} \right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[x^n*y''[x]+(a*x^(n-1)+b*x)*y'[x]+(a-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved