14.3.5 problem 7

Internal problem ID [2514]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.9. Exact equations. Excercises page 66
Problem number : 7
Date solved : Monday, January 27, 2025 at 05:56:54 AM
CAS classification : [_separable]

\begin{align*} 2 t y^{3}+3 t^{2} y^{2} y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 7

dsolve([(2*t*y(t)^3)+(3*t^2*y(t)^2)*diff(y(t),t)=0,y(1) = 1],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 10

DSolve[{(2*t*y[t]^3)+(3*t^2*y[t]^2)*D[y[t],t]==0,{y[1]==1}},y[t],t,IncludeSingularSolutions -> True]
 

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