Internal problem ID [11064]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev.
Second edition
Section: Chapter 2, Second-Order Differential Equations. section 2.1.2-8. Other equations.
Problem number: 239.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{6} y^{\prime \prime }+\left (3 x^{2}+a \right ) x^{3} y^{\prime }+y b=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 45
dsolve(x^6*diff(y(x),x$2)+(3*x^2+a)*x^3*diff(y(x),x)+b*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {-a +\sqrt {a^{2}-4 b}}{4 x^{2}}}+c_{2} {\mathrm e}^{\frac {a +\sqrt {a^{2}-4 b}}{4 x^{2}}} \]
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 56
DSolve[x^6*y''[x]+(3*x^2+a)*x^3*y'[x]+b*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{\frac {a-\sqrt {a^2-4 b}}{4 x^2}} \left (c_1 e^{\frac {\sqrt {a^2-4 b}}{2 x^2}}+c_2\right ) \]