27.22 problem 32

Internal problem ID [10856]

Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.2-2 Equation of form \(y''+f(x)y'+g(x)y=0\)
Problem number: 32.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

\[ \boxed {y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c \left (-c \,x^{2 n}+a \,x^{1+n}+b \,x^{n}+n \,x^{n -1}\right ) y=0} \]

✗ Solution by Maple

dsolve(diff(y(x),x$2)+(a*x+b)*diff(y(x),x)+c*(-c*x^(2*n)+a*x^(n+1)+b*x^n+n*x^(n-1) )*y(x)=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.0 (sec). Leaf size: 0

DSolve[y''[x]+(a*x+b)*y'[x]+c*(-c*x^(2*n)+a*x^(n+1)+b*x^n+n*x^(n-1) )*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

Not solved