48.3.5 problem Example 3.34

Internal problem ID [7529]
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
Date solved : Monday, January 27, 2025 at 03:04:40 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=4 \,{\mathrm e}^{t} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 22

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)
 

\[ y = {\mathrm e}^{t} \left (\frac {2}{3} t^{3}+c_{1} +t c_{2} +t^{2} c_3 \right ) \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 34

DSolve[D[ y[t],{t,3}]-3*D[y[t],{t,2}]+3*D[y[t],t]-y[t]==4*Exp[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{3} e^t \left (2 t^3+3 c_3 t^2+3 c_2 t+3 c_1\right ) \]