12.8.19 problem 22

Internal problem ID [1755]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.1 Homogeneous linear equations. Page 203
Problem number : 22
Date solved : Tuesday, January 28, 2025 at 02:35:53 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x +1\right ) y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (1+x \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.143 (sec). Leaf size: 32

dsolve((2*x+1)*diff(y(x),x$2)-2*(2*x^2-1)*diff(y(x),x)-4*(x+1)*y(x)=0,y(x), singsol=all)
 

\[ y = c_1 \operatorname {HeunB}\left (-\frac {1}{2}, -2, -\frac {1}{2}, 3, x +\frac {1}{2}\right )+c_2 \operatorname {HeunB}\left (\frac {1}{2}, -2, -\frac {1}{2}, 3, x +\frac {1}{2}\right ) \sqrt {4 x +2} \]

✗ Solution by Mathematica

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

DSolve[(2*x+1)*D[y[x],{x,2}]-2*(2*x^2-1)*D[y[x],x]-4*(x+1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved