60.3.300 problem 1306

Internal problem ID [11310]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1306
Date solved : Tuesday, January 28, 2025 at 05:58:13 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.734 (sec). Leaf size: 69

dsolve(x^3*diff(diff(y(x),x),x)+x^2*diff(y(x),x)+(a*x^2+b*x+a)*y(x)=0,y(x), singsol=all)
 

\[ y = \operatorname {HeunD}\left (0, 8 a +4 b , 0, 8 a -4 b , \frac {x +1}{x -1}\right ) \left (c_{1} +c_{2} \left (\int \frac {1}{x \operatorname {HeunD}\left (0, 8 a +4 b , 0, 8 a -4 b , \frac {x +1}{x -1}\right )^{2}}d x \right )\right ) \]

✗ Solution by Mathematica

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

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

Not solved