Internal problem ID [1682]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.4. Page 24
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (t -\sqrt {y t}\right ) y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve((t-sqrt(t*y(t)))*diff(y(t),t)=y(t),y(t), singsol=all)
\[ \ln \left (y \relax (t )\right )+\frac {2 t}{\sqrt {t y \relax (t )}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.208 (sec). Leaf size: 31
DSolve[(t-Sqrt[t*y[t]])*y'[t]==y[t],y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2}{\sqrt {\frac {y(t)}{t}}}+\log \left (\frac {y(t)}{t}\right )=-\log (t)+c_1,y(t)\right ] \]