74.11.16 problem 28

Internal problem ID [16266]
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 : 28
Date solved : Tuesday, January 28, 2025 at 08:59:26 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 16 y^{\prime \prime }-8 y^{\prime }-15 y&=75 t \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 34

dsolve(16*diff(y(t),t$2)-8*diff(y(t),t)-15*y(t)=75*t,y(t), singsol=all)
 

\[ y = -\frac {\left (-3 c_{1} {\mathrm e}^{2 t}+15 t \,{\mathrm e}^{\frac {3 t}{4}}-8 \,{\mathrm e}^{\frac {3 t}{4}}-3 c_{2} \right ) {\mathrm e}^{-\frac {3 t}{4}}}{3} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 32

DSolve[16*D[y[t],{t,2}]-8*D[y[t],t]-15*y[t]==75*t,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -5 t+c_1 e^{-3 t/4}+c_2 e^{5 t/4}+\frac {8}{3} \]