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]]
Solve \begin {gather*} \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} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= [t^{2}, t^{3}] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \relax (t ) = c_{1} t^{2}+c_{2} t^{3}+c_{3} \left (t +1\right ) \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 53
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]
\begin{align*} y(t)\to \frac {1}{8} \left (-4 c_2 \left (t^3-3 t^2+t+1\right )+c_3 (3 t+1) (t-1)^2+2 c_1 (t ((t-3) t+3)+3)\right ) \\ \end{align*}