11.1.9 problem 20

Internal problem ID [1470]
Book : Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima, Meade
Section : Chapter 4.1, Higher order linear differential equations. General theory. page 173
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 02:35:39 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 16

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

\[ y = \left (c_3 t +c_2 \right ) {\mathrm e}^{t}+c_1 t \]

✓ Solution by Mathematica

Time used: 0.101 (sec). Leaf size: 28

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

\[ y(t)\to t \left (c_2 e^t+c_1\right )+(c_3-4 c_2) e^t \]