Internal problem ID [5863]
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]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y=g \left (t \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 64
dsolve(diff(y(t),t$3)-diff(y(t),t$2)-diff(y(t),t)+y(t)=g(t),y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\left (\int \left (2 t +1\right ) g \left (t \right ) {\mathrm e}^{-t}d t \right ) {\mathrm e}^{t}}{4}+\frac {\left (\int {\mathrm e}^{-t} g \left (t \right )d t \right ) {\mathrm e}^{t} t}{2}+\frac {\left (\int {\mathrm e}^{t} g \left (t \right )d t \right ) {\mathrm e}^{-t}}{4}+c_{2} {\mathrm e}^{-t}+{\mathrm e}^{t} \left (c_{3} t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 106
DSolve[y'''[t]-y''[t]-y'[t]+y[t]==g[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-t} \int _1^t\frac {1}{4} e^{K[1]} g(K[1])dK[1]+e^t t \int _1^t\frac {1}{2} e^{-K[3]} g(K[3])dK[3]+e^t \int _1^t-\frac {1}{4} e^{-K[2]} g(K[2]) (2 K[2]+1)dK[2]+c_1 e^{-t}+c_2 e^t+c_3 e^t t \]