Internal problem ID [5110]
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 3.36.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y-g \relax (t )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 66
dsolve(diff(y(t),t$3)-diff(y(t),t$2)-diff(y(t),t)+y(t)=g(t),y(t), singsol=all)
\[ y \relax (t ) = -\left (\int \frac {\left (2 t +1\right ) g \relax (t ) {\mathrm e}^{-t}}{4}d t \right ) {\mathrm e}^{t}+\left (\int \frac {{\mathrm e}^{t} g \relax (t )}{4}d t \right ) {\mathrm e}^{-t}+\left (\int \frac {{\mathrm e}^{-t} g \relax (t )}{2}d t \right ) {\mathrm e}^{t} t +c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{t} t \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 92
DSolve[y'''[t]-y''[t]-y'[t]+y[t]==g[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-t} \left (\int _1^t\frac {1}{4} e^{K[1]} g(K[1])dK[1]+c_1\right )+e^t \left (t \int _1^t\frac {1}{2} e^{-K[3]} g(K[3])dK[3]+\int _1^t-\frac {1}{4} e^{-K[2]} g(K[2]) (2 K[2]+1)dK[2]+c_3 t+c_2\right ) \\ \end{align*}