Internal problem ID [821]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {t^{2} \left (t +3\right ) y^{\prime \prime \prime }-3 t \left (t +2\right ) y^{\prime \prime }+6 \left (1+t \right ) y^{\prime }-6 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
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,[t^2,t^3]],y(t), singsol=all)
\[ y \left (t \right ) = c_{1} t^{2}+t^{3} c_{2} +c_{3} \left (t +1\right ) \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 58
DSolve[t^2*(t+3)*y'''[t]-3*t*(t+2)*y''[t]+6*(1+t)*y'[t]-6*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{8} \left (2 c_1 \left (t^3-3 t^2+3 t+3\right )-(t-1) \left (4 c_2 \left (t^2-2 t-1\right )+c_3 \left (-3 t^2+2 t+1\right )\right )\right ) \]