2.6 problem 6

Internal problem ID [1654]

Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 9
Problem number: 6.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

\[ \boxed {y t^{2}+y^{\prime }=t^{2}} \]

✓ Solution by Maple

Time used: 0.0 (sec). Leaf size: 14

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

\[ y \left (t \right ) = 1+{\mathrm e}^{-\frac {t^{3}}{3}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 24

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