72.8.16 problem 29

Internal problem ID [14780]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Review Exercises for chapter 1. page 136
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 07:15:09 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=-3 y+{\mathrm e}^{-2 t}+t^{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 24

dsolve(diff(y(t),t)= -3*y(t)+exp(-2*t)+t^2,y(t), singsol=all)
 

\[ y = \frac {t^{2}}{3}-\frac {2 t}{9}+\frac {2}{27}+{\mathrm e}^{-2 t}+{\mathrm e}^{-3 t} c_{1} \]

✓ Solution by Mathematica

Time used: 0.205 (sec). Leaf size: 37

DSolve[D[y[t],t]==-3*y[t]+Exp[-2*t]+t^2,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-3 t} \left (\int _1^t\left (e^{3 K[1]} K[1]^2+e^{K[1]}\right )dK[1]+c_1\right ) \]