14.1.6 problem 6

Internal problem ID [2477]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.2. Linear equations. Excercises page 9
Problem number : 6
Date solved : Monday, January 27, 2025 at 05:53:43 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

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

\[ y = 1+{\mathrm e}^{-\frac {t^{3}}{3}} c_1 \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 24

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

\begin{align*} y(t)\to 1+c_1 e^{-\frac {t^3}{3}} \\ y(t)\to 1 \\ \end{align*}