74.11.6 problem 18

Internal problem ID [16256]
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 : 18
Date solved : Tuesday, January 28, 2025 at 08:58:50 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }&=3-4 t \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(t),t$2)+2*diff(y(t),t)=3-4*t,y(t), singsol=all)
 

\[ y = -\frac {c_{1} {\mathrm e}^{-2 t}}{2}-t^{2}+\frac {5 t}{2}+c_{2} \]

✓ Solution by Mathematica

Time used: 4.794 (sec). Leaf size: 46

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

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