Internal problem ID [820]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (2-t \right ) y^{\prime \prime \prime }+\left (2 t -3\right ) y^{\prime \prime }-y^{\prime } t +y=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{t} \end {align*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 17
dsolve([(2-t)*diff(y(t),t$3)+(2*t-3)*diff(y(t),t$2)-t*diff(y(t),t)+y(t)=0,exp(t)],y(t), singsol=all)
\[ y \relax (t ) = c_{1} t +c_{2} {\mathrm e}^{t}+c_{3} {\mathrm e}^{t} t \]
✓ Solution by Mathematica
Time used: 0.07 (sec). Leaf size: 23
DSolve[(2-t)*y'''[t]+(2*t-3)*y''[t]-t*y'[t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_1 t+e^t (c_2 (t-4)+c_3) \\ \end{align*}