72.8.30 problem 45

Internal problem ID [14794]
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 : 45
Date solved : Tuesday, January 28, 2025 at 07:15:46 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

\[ y = -1+{\mathrm e}^{\frac {t \left (t^{2}+3\right )}{3}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.299 (sec). Leaf size: 26

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

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