Internal problem ID [14846]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+5 y^{\prime }=5 t^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(t),t$2)+5*diff(y(t),t)=5*t^2,y(t), singsol=all)
\[ y \left (t \right ) = -\frac {t^{2}}{5}+\frac {t^{3}}{3}-\frac {{\mathrm e}^{-5 t} c_{1}}{5}+\frac {2 t}{25}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 38
DSolve[y''[t]+5*y'[t]==5*t^2,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {t^3}{3}-\frac {t^2}{5}+\frac {2 t}{25}-\frac {1}{5} c_1 e^{-5 t}+c_2 \]