74.7.28 problem 28

Internal problem ID [16105]
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 : 28
Date solved : Tuesday, January 28, 2025 at 08:41:19 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y-\left (3 \sqrt {t y}+t \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 21

dsolve(y(t)-(3*sqrt(t*y(t))+t)*diff(y(t),t)=0,y(t), singsol=all)
 

\[ 3 \ln \left (y\right )-\frac {2 t}{\sqrt {t y}}-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.223 (sec). Leaf size: 33

DSolve[y[t]-(3*Sqrt[t*y[t]]+t)*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [3 \log \left (\frac {y(t)}{t}\right )-\frac {2}{\sqrt {\frac {y(t)}{t}}}=-3 \log (t)+c_1,y(t)\right ] \]