64.22.4 problem 1 (d)

Internal problem ID [13669]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 11, The nth order homogeneous linear differential equation. Section 11.8, Exercises page 583
Problem number : 1 (d)
Date solved : Tuesday, January 28, 2025 at 05:54:41 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} t^{3} x^{\prime \prime }-\left (t^{3}+2 t^{2}-t \right ) x^{\prime }+\left (t^{2}+t -1\right ) x&=0 \end{align*}

✓ Solution by Maple

Time used: 1.313 (sec). Leaf size: 47

dsolve(t^3*diff(x(t),t$2)-(t^3+2*t^2-t)*diff(x(t),t)+(t^2+t-1)*x(t)=0,x(t), singsol=all)
 

\[ x \left (t \right ) = \left ({\mathrm e}^{t} \operatorname {HeunD}\left (-4, -5, 8, -3, \frac {t -1}{t +1}\right ) c_{2} +\operatorname {HeunD}\left (4, -5, 8, -3, \frac {t -1}{t +1}\right ) {\mathrm e}^{\frac {1}{t}} c_{1} \right ) t^{{3}/{2}} \]

✓ Solution by Mathematica

Time used: 0.260 (sec). Leaf size: 34

DSolve[t^3*D[x[t],{t,2}]-(t^3+2*t^2-t)*D[x[t],t]+(t^2+t-1)*x[t]==0,{x[t]},t,IncludeSingularSolutions -> True]
 

\[ x(t)\to e^t t \left (c_2 \int _1^te^{\frac {1}{K[1]}-K[1]}dK[1]+c_1\right ) \]