74.18.19 problem 25

Internal problem ID [16576]
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
Date solved : Tuesday, January 28, 2025 at 09:11:10 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }&=5 t^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve(diff(y(t),t$2)+5*diff(y(t),t)=5*t^2,y(t), singsol=all)
 

\[ y = -\frac {t^{2}}{5}+\frac {t^{3}}{3}-\frac {{\mathrm e}^{-5 t} c_{1}}{5}+\frac {2 t}{25}+c_{2} \]

✓ Solution by Mathematica

Time used: 4.835 (sec). Leaf size: 45

DSolve[D[y[t],{t,2}]+5*D[y[t],t]==5*t^2,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _1^te^{-5 K[2]} \left (c_1+\int _1^{K[2]}5 e^{5 K[1]} K[1]^2dK[1]\right )dK[2]+c_2 \]