72.2.20 problem 16 (v)

Internal problem ID [14655]
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. Exercises section 1.3 page 47
Problem number : 16 (v)
Date solved : Tuesday, January 28, 2025 at 06:46:36 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.283 (sec). Leaf size: 46

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

\begin{align*} y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1] (K[1]+1)}dK[1]\&\right ]\left [\frac {t^2}{2}+c_1\right ] \\ y(t)\to -1 \\ y(t)\to 0 \\ \end{align*}