Internal problem ID [1105]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (1+2 x \right ) y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (x +1\right ) y=0} \]
✓ Solution by Maple
Time used: 0.187 (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)
\[ y \left (x \right ) = c_{1} \operatorname {HeunB}\left (-\frac {1}{2}, -2, -\frac {1}{2}, 3, x +\frac {1}{2}\right )+c_{2} \operatorname {HeunB}\left (\frac {1}{2}, -2, -\frac {1}{2}, 3, x +\frac {1}{2}\right ) \sqrt {4 x +2} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(2*x+1)*y''[x]-2*(2*x^2-1)*y'[x]-4*(x+1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved