61.31.25 problem 206

Internal problem ID [12706]
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
Problem number : 206
Date solved : Tuesday, January 28, 2025 at 03:54:09 AM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 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 }+\lambda y&=0 \end{align*}

✓ Solution by Maple

Time used: 1.450 (sec). Leaf size: 65

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)
 

\[ y = c_{1} {\mathrm e}^{\frac {i \sqrt {2}\, \sqrt {\lambda }\, \left (\int \frac {1}{\sqrt {a \,x^{3}+b \,x^{2}+c x +d}}d x \right )}{2}}+c_{2} {\mathrm e}^{-\frac {i \sqrt {2}\, \sqrt {\lambda }\, \left (\int \frac {1}{\sqrt {a \,x^{3}+b \,x^{2}+c x +d}}d x \right )}{2}} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[2*(a*x^3+b*x^2+c*x+d)*D[y[x],{x,2}]+(3*a*x^2+2*b*x+c)*D[y[x],x]+lambda*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Timed out