74.11.38 problem 50

Internal problem ID [16288]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 50
Date solved : Tuesday, January 28, 2025 at 09:00:35 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=3 t \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {23}{12}}\\ y^{\prime }\left (0\right )&=-{\frac {3}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 26

dsolve([diff(y(t),t$2)+diff(y(t),t)-6*y(t)=3*t,y(0) = 23/12, D(y)(0) = -3/2],y(t), singsol=all)
 

\[ y = -\frac {\left (\left (t +\frac {1}{6}\right ) {\mathrm e}^{3 t}-2 \,{\mathrm e}^{5 t}-2\right ) {\mathrm e}^{-3 t}}{2} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 24

DSolve[{D[y[t],{t,2}]+D[y[t],t]-6*y[t]==3*t,{y[0]==23/12,Derivative[1][y][0] ==-3/2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {t}{2}+e^{-3 t}+e^{2 t}-\frac {1}{12} \]