Internal problem ID [14524]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }=-4 t +3} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(diff(y(t),t$2)+2*diff(y(t),t)=3-4*t,y(t), singsol=all)
\[ y \left (t \right ) = -\frac {{\mathrm e}^{-2 t} c_{1}}{2}-t^{2}+\frac {5 t}{2}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.109 (sec). Leaf size: 29
DSolve[y''[t]+2*y'[t]==3-4*t,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -t^2+\frac {5 t}{2}-\frac {1}{2} c_1 e^{-2 t}+c_2 \]