61.31.24 problem 205

Internal problem ID [12705]
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 : 205
Date solved : Tuesday, January 28, 2025 at 08:11:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }-\left (-\lambda ^{2}+x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 1.524 (sec). Leaf size: 84

dsolve((a*x^3+b*x^2+c*x+d)*diff(y(x),x$2)-(x^2-lambda^2)*diff(y(x),x)+(x+lambda)*y(x)=0,y(x), singsol=all)
 

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

✗ Solution by Mathematica

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

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

Timed out