Internal problem ID [14534]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {16 y^{\prime \prime }-8 y^{\prime }-15 y=75 t} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (t \right ) = \frac {\left (3 c_{2} {\mathrm e}^{2 t}-15 t \,{\mathrm e}^{\frac {3 t}{4}}+8 \,{\mathrm e}^{\frac {3 t}{4}}+3 c_{1} \right ) {\mathrm e}^{-\frac {3 t}{4}}}{3} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 32
DSolve[16*y''[t]-8*y'[t]-15*y[t]==75*t,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -5 t+c_1 e^{-3 t/4}+c_2 e^{5 t/4}+\frac {8}{3} \]