48.3.7 problem Example 3.36

Internal problem ID [7531]
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
Date solved : Monday, January 27, 2025 at 03:04:42 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=g \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (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)
 

\[ y = -\frac {\left (\int \left (2 t +1\right ) g \left (t \right ) {\mathrm e}^{-t}d t \right ) {\mathrm e}^{t}}{4}+\frac {\left (\int {\mathrm e}^{-t} g \left (t \right )d t \right ) {\mathrm e}^{t} t}{2}+\frac {\left (\int {\mathrm e}^{t} g \left (t \right )d t \right ) {\mathrm e}^{-t}}{4}+c_{2} {\mathrm e}^{-t}+{\mathrm e}^{t} \left (t c_3 +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 106

DSolve[D[ y[t],{t,3}]-D[y[t],{t,2}]-D[y[t],t]+y[t]==g[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t} \int _1^t\frac {1}{4} e^{K[1]} g(K[1])dK[1]+e^t t \int _1^t\frac {1}{2} e^{-K[3]} g(K[3])dK[3]+e^t \int _1^t-\frac {1}{4} e^{-K[2]} g(K[2]) (2 K[2]+1)dK[2]+c_1 e^{-t}+c_2 e^t+c_3 e^t t \]