74.7.39 problem 39

Internal problem ID [16116]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 39
Date solved : Tuesday, January 28, 2025 at 08:47:41 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.115 (sec). Leaf size: 14

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

\[ y = \left (-3 \ln \left (t \right )+27\right )^{{1}/{3}} t \]

✓ Solution by Mathematica

Time used: 0.195 (sec). Leaf size: 22

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

\[ y(t)\to \sqrt [3]{3} t \sqrt [3]{9-\log (t)} \]