Internal problem ID [11073]
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: 249.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (a \,x^{n}+b \right ) y^{\prime \prime }+\left (x^{n} c +d \right ) y^{\prime }+\lambda \left (\left (-a \lambda +c \right ) x^{n}+d -b \lambda \right ) y=0} \]
✗ Solution by Maple
dsolve((a*x^n+b)*diff(y(x),x$2)+(c*x^n+d)*diff(y(x),x)+lambda*((c-a*lambda)*x^n+d-b*lambda)*y(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(a*x^n+b)*y''[x]+(c*x^n+d)*y'[x]+\[Lambda]*((c-a*\[Lambda])*x^n+d-b*\[Lambda])*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved