Internal problem ID [11030]
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: 206.
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)]`]]
\[ \boxed {2 \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (3 a \,x^{2}+2 b x +c \right ) y^{\prime }+y \lambda =0} \]
✓ Solution by Maple
Time used: 0.453 (sec). Leaf size: 67
dsolve(2*(a*x^3+b*x^2+c*x+d)*diff(y(x),x$2)+(3*a*x^2+2*b*x+c)*diff(y(x),x)+lambda*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{\frac {i \sqrt {2}\, \sqrt {\lambda }\, \left (\int \frac {1}{\sqrt {a \,x^{3}+x^{2} b +c x +d}}d x \right )}{2}}+c_{2} {\mathrm e}^{-\frac {i \sqrt {2}\, \sqrt {\lambda }\, \left (\int \frac {1}{\sqrt {a \,x^{3}+x^{2} b +c x +d}}d x \right )}{2}} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[2*(a*x^3+b*x^2+c*x+d)*y''[x]+(3*a*x^2+2*b*x+c)*y'[x]+lambda*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Timed out