Internal problem ID [10097]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second
edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.2-1 Equation of form
\(y''+f(x)y'+g(x)y=0\)
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}+x^{n} a +x^{n -1} n \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 47
dsolve(diff(y(x),x$2)+a*diff(y(x),x)+b*(-b*x^(2*n)+a*x^n+n*x^(n-1))*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \left (\left (\int {\mathrm e}^{-x a} {\mathrm e}^{\frac {2 x^{n +1} b}{n +1}}d x \right ) c_{1}+c_{2}\right ) {\mathrm e}^{-\frac {x^{n +1} b}{n +1}} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x]+a*y'[x]+b*(-b*x^(2*n)+a*x^n+n*x^(n-1))*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved