90.6.10 problem 10

Internal problem ID [25154]
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 : 10
Date solved : Thursday, October 02, 2025 at 11:55:11 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} a t +b y-\left (c t +d y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.121 (sec). Leaf size: 147

ode:=a*t+b*y(t)-(c*t+d*y(t))*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = -\frac {t \left (\sqrt {-4 a d -b^{2}+2 b c -c^{2}}\, \tan \left (\operatorname {RootOf}\left (\sqrt {-4 a d -b^{2}+2 b c -c^{2}}\, \ln \left (-\frac {t^{2} \left (4 a d +b^{2}-2 b c +c^{2}\right ) \sec \left (\textit {\_Z} \right )^{2}}{d}\right )-2 \sqrt {-4 a d -b^{2}+2 b c -c^{2}}\, \ln \left (2\right )+2 c_1 \sqrt {-4 a d -b^{2}+2 b c -c^{2}}-2 \textit {\_Z} b -2 \textit {\_Z} c \right )\right )-b +c \right )}{2 d} \]

✓ Mathematica. Time used: 0.154 (sec). Leaf size: 110

ode=(a*t+b*y[t])-(c*t+d*y[t])*D[y[t],t]== 0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {(b+c) \arctan \left (\frac {-b+c+\frac {2 d y(t)}{t}}{\sqrt {-4 a d-b^2+2 b c-c^2}}\right )}{\sqrt {-4 a d-b^2+2 b c-c^2}}+\frac {1}{2} \log \left (-a-\frac {b y(t)}{t}+\frac {c y(t)}{t}+\frac {d y(t)^2}{t^2}\right )=-\log (t)+c_1,y(t)\right ] \]

✗ Sympy

from sympy import * 
t = symbols("t") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
d = symbols("d") 
y = Function("y") 
ode = Eq(a*t + b*y(t) - (c*t + d*y(t))*Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

RecursionError : maximum recursion depth exceeded