90.6.5 problem 5

Internal problem ID [25149]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 83
Problem number : 5
Date solved : Thursday, October 02, 2025 at 11:54:53 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 y-5 t +2 y y^{\prime }-t y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.221 (sec). Leaf size: 55

ode:=3*y(t)-5*t+2*y(t)*diff(y(t),t)-t*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ -\frac {\ln \left (\frac {-5 t^{2}+2 t y+2 y^{2}}{t^{2}}\right )}{2}-\frac {2 \sqrt {11}\, \operatorname {arctanh}\left (\frac {\left (2 y+t \right ) \sqrt {11}}{11 t}\right )}{11}-\ln \left (t \right )-c_1 = 0 \]

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 68

ode=(3*y[t]-5*t)+2*y[t]*D[y[t],t]-t*D[y[t],t]== 0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {1}{22} \left (11-2 \sqrt {11}\right ) \log \left (-\frac {2 y(t)}{t}+\sqrt {11}-1\right )+\frac {1}{22} \left (11+2 \sqrt {11}\right ) \log \left (\frac {2 y(t)}{t}+\sqrt {11}+1\right )=-\log (t)+c_1,y(t)\right ] \]

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t*Derivative(y(t), t) - 5*t + 2*y(t)*Derivative(y(t), t) + 3*y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out