72.8.2 problem 3

Internal problem ID [14766]
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. Review Exercises for chapter 1. page 136
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 07:14:34 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=t^{2} \left (t^{2}+1\right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

dsolve(diff(y(t),t)=t^2*(t^2+1),y(t), singsol=all)
 

\[ y = \frac {1}{5} t^{5}+\frac {1}{3} t^{3}+c_{1} \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 22

DSolve[D[y[t],t]==t^2*(t^2+1),y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {t^5}{5}+\frac {t^3}{3}+c_1 \]