72.2.21 problem 16 (vi)

Internal problem ID [14656]
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 (vi)
Date solved : Tuesday, January 28, 2025 at 06:46:39 AM
CAS classification : [_separable]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 24

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

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