74.6.30 problem 31

Internal problem ID [16053]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 31
Date solved : Tuesday, January 28, 2025 at 08:31:54 AM
CAS classification : [_separable]

\begin{align*} 2 t y^{2}+2 t^{2} y y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 7

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

\[ y = \frac {1}{t} \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 8

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

\[ y(t)\to \frac {1}{t} \]