Internal problem ID [5861]
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]]
\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y=4 \,{\mathrm e}^{t}} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (t \right ) = {\mathrm e}^{t} \left (\frac {2}{3} t^{3}+c_{1} +t c_{2} +t^{2} c_{3} \right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 34
DSolve[y'''[t]-3*y''[t]+3*y'[t]-y[t]==4*Exp[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{3} e^t \left (2 t^3+3 c_3 t^2+3 c_2 t+3 c_1\right ) \]