Internal problem ID [11085]
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: 261.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda -x \right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.781 (sec). Leaf size: 68
dsolve((a*x^n+b*x^m+c)*diff(y(x),x$2)+(lambda-x)*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\left (\left (\int {\mathrm e}^{\int \frac {-2 a \,x^{n}-2 b \,x^{m}-2 c +x^{2}-2 x \lambda +\lambda ^{2}}{\left (a \,x^{n}+b \,x^{m}+c \right ) \left (-\lambda +x \right )}d x}d x \right ) c_{1} +c_{2} \right ) \left (\lambda -x \right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(a*x^n+b*x^m+c)*y''[x]+(\[Lambda]-x)*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved