Internal problem ID [5108]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T.
CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.5 HIGHER ORDER ODE. Page
181
Problem number: Example 3.34.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y-4 \,{\mathrm e}^{t}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(diff(y(t),t$3)-3*diff(y(t),t$2)+3*diff(y(t),t)-y(t)=4*exp(t),y(t), singsol=all)
\[ y \relax (t ) = \frac {2 \,{\mathrm e}^{t} t^{3}}{3}+c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{t} t +c_{3} {\mathrm e}^{t} t^{2} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 34
DSolve[y'''[t]-3*y''[t]+3*y'[t]-y[t]==4*Exp[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{3} e^t \left (2 t^3+3 c_3 t^2+3 c_2 t+3 c_1\right ) \\ \end{align*}