Internal problem ID [11025]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev.
Second edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.2-6 Equation of form
\((a_3 x^3+a_2 x^2 x+a_1 x+a_0) y''+f(x)y'+g(x)y=0\)
Problem number: 201.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (a \,x^{3}+x^{2}+b \right ) y^{\prime \prime }+a^{2} x \left (x^{2}-b \right ) y^{\prime }-a^{3} b x y=0} \]
✓ Solution by Maple
Time used: 0.562 (sec). Leaf size: 79
dsolve((a*x^3+x^2+b)*diff(y(x),x$2)+a^2*x*(x^2-b)*diff(y(x),x)-a^3*b*x*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-a x} \left (c_{2} \left (\int {\mathrm e}^{a \left (\int \frac {a^{2} x^{4}+2 a \,x^{3}+\left (a^{2} b +2\right ) x^{2}+4 a b x +2 b}{\left (a \,x^{3}+x^{2}+b \right ) \left (a x +2\right )}d x \right )}d x \right )+c_{1} \right ) \left (a x +2\right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(a*x^3+x^2+b)*y''[x]+a^2*x*(x^2-b)*y'[x]-a^3*b*x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Timed out