72.8.24 problem 37

Internal problem ID [14788]
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 : 37
Date solved : Tuesday, January 28, 2025 at 07:15:31 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 16

dsolve([diff(y(t),t)= 2*t*y(t)^2+3*t^2*y(t)^2,y(1) = -1],y(t), singsol=all)
 

\[ y = -\frac {1}{t^{3}+t^{2}-1} \]

✓ Solution by Mathematica

Time used: 0.155 (sec). Leaf size: 17

DSolve[{D[y[t],t]== 2*t*y[t]^2+3*t^2*y[t]^2,{y[1]==-1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {1}{t^3+t^2-1} \]