13.2.6 problem 6

Internal problem ID [2304]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 9
Problem number : 6
Date solved : Monday, January 27, 2025 at 05:45:04 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 24

DSolve[t^2*y[t]+D[y[t],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*}