74.3.31 problem 26

Internal problem ID [15891]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 08:17:31 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.051 (sec). Leaf size: 13

dsolve([diff(y(t),t)=t*y(t)^2,y(0) = 1/2],y(t), singsol=all)
 

\[ y = -\frac {2}{t^{2}-4} \]

✓ Solution by Mathematica

Time used: 0.129 (sec). Leaf size: 14

DSolve[{D[y[t],t]==t*y[t]^2,{y[0]==1/2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {2}{t^2-4} \]