73.9.2 problem 14.1 (b)

Internal problem ID [15263]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 14. Higher order equations and the reduction of order method. Additional exercises page 277
Problem number : 14.1 (b)
Date solved : Tuesday, January 28, 2025 at 08:25:32 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+x^{2} y^{\prime }-4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.870 (sec). Leaf size: 54

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

\[ y = {\mathrm e}^{-\frac {x^{3}}{3}} \operatorname {HeunT}\left (-4 \,3^{{2}/{3}}, -3, 0, \frac {3^{{2}/{3}} x}{3}\right ) \left (c_{1} +c_{2} \left (\int \frac {{\mathrm e}^{\frac {x^{3}}{3}}}{\operatorname {HeunT}\left (-4 \,3^{{2}/{3}}, -3, 0, \frac {3^{{2}/{3}} x}{3}\right )^{2}}d x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 35

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

\[ y(x)\to c_2 e^{-\frac {x^3}{3}} \text {HeunT}[4,-2,0,0,-1,x]+c_1 \text {HeunT}[4,0,0,0,1,x] \]