Internal problem ID [11016]
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: 192.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (a x +b \right ) y^{\prime \prime }-2 x \left (a x +2 b \right ) y^{\prime }+2 \left (a x +3 b \right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve(x^2*(a*x+b)*diff(y(x),x$2)-2*x*(a*x+2*b)*diff(y(x),x)+2*(a*x+3*b)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{2} \left (c_{2} x +c_{1} \right )}{a x +b} \]
✓ Solution by Mathematica
Time used: 0.068 (sec). Leaf size: 23
DSolve[x^2*(a*x+b)*y''[x]-2*x*(a*x+2*b)*y'[x]+2*(a*x+3*b)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^2 (c_2 x+c_1)}{a x+b} \]