72.8.26 problem 39

Internal problem ID [14790]
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 : 39
Date solved : Tuesday, January 28, 2025 at 07:15:35 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {t^{2}}{y+t^{3} y} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 18

dsolve([diff(y(t),t)= t^2/(y(t)+t^3*y(t)),y(0) = -2],y(t), singsol=all)
 

\[ y = -\frac {\sqrt {36+6 \ln \left (t^{3}+1\right )}}{3} \]

✓ Solution by Mathematica

Time used: 0.099 (sec). Leaf size: 26

DSolve[{D[y[t],t]== t^2/(y[t]+t^3*y[t]),{y[0]==-2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\sqrt {\frac {2}{3}} \sqrt {\log \left (t^3+1\right )+6} \]