14.2.16 problem 17

Internal problem ID [2504]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.4 separable equations. Excercises page 24
Problem number : 17
Date solved : Monday, January 27, 2025 at 05:56:06 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 19

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

\[ \ln \left (y\right )+\frac {2 t}{\sqrt {t y}}-c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.234 (sec). Leaf size: 31

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

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