11.1.10 problem 21

Internal problem ID [1471]
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 : 21
Date solved : Tuesday, January 28, 2025 at 02:35:39 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} t^{2} \left (t +3\right ) y^{\prime \prime \prime }-3 t \left (t +2\right ) y^{\prime \prime }+6 \left (1+t \right ) y^{\prime }-6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 19

dsolve(t^2*(t+3)*diff(y(t),t$3)-3*t*(t+2)*diff(y(t),t$2)+6*(1+t)*diff(y(t),t)-6*y(t)=0,y(t), singsol=all)
 

\[ y = c_2 \,t^{3}+c_1 \,t^{2}+c_3 t +c_3 \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 58

DSolve[t^2*(t+3)*D[ y[t],{t,3}]-3*t*(t+2)*D[y[t],{t,2}]+6*(1+t)*D[y[t],t]-6*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{8} \left (2 c_1 \left (t^3-3 t^2+3 t+3\right )-(t-1) \left (4 c_2 \left (t^2-2 t-1\right )+c_3 \left (-3 t^2+2 t+1\right )\right )\right ) \]