Internal problem ID [10878]
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: 54.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+x^{n} \left (a \,x^{2}+\left (a c +b \right ) x +b c \right ) y^{\prime }-x^{n} \left (a x +b \right ) y=0} \]
✓ Solution by Maple
Time used: 0.484 (sec). Leaf size: 78
dsolve(diff(y(x),x$2)+x^n*(a*x^2+(a*c+b)*x+b*c)*diff(y(x),x)-x^n*(a*x+b)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\left (x +c \right ) \left (\left (\int \frac {{\mathrm e}^{-\frac {\left (a \,x^{2} \left (n +2\right ) \left (n +1\right )+\left (a c +b \right ) x \left (3+n \right ) \left (n +1\right )+b c \left (3+n \right ) \left (n +2\right )\right ) x^{n +1}}{\left (3+n \right ) \left (n +1\right ) \left (n +2\right )}}}{\left (x +c \right )^{2}}d x \right ) c_{1} +c_{2} \right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x]+x^n*(a*x^2+(a*c+b)*x+b*c)*y'[x]-x^n*(a*x+b)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved