90.3.4 problem 4

Internal problem ID [25068]
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 41
Problem number : 4
Date solved : Thursday, October 02, 2025 at 11:48:13 PM
CAS classification : [_Bernoulli]

\begin{align*} \frac {y^{\prime }}{y}&=y-t \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 32

ode:=diff(y(t),t)/y(t) = y(t)-t; 
dsolve(ode,y(t), singsol=all);
 

\[ y = -\frac {2 \,{\mathrm e}^{-\frac {t^{2}}{2}}}{\sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {\sqrt {2}\, t}{2}\right )-2 c_1} \]

✓ Mathematica. Time used: 0.114 (sec). Leaf size: 45

ode=D[y[t],{t,1}]/y[t]==y[t]-t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {2 e^{-\frac {t^2}{2}}}{-\sqrt {2 \pi } \text {erf}\left (\frac {t}{\sqrt {2}}\right )+2 c_1}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.235 (sec). Leaf size: 32

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

\[ y{\left (t \right )} = \frac {2 e^{- \frac {t^{2}}{2}}}{C_{1} - \sqrt {2} \sqrt {\pi } \operatorname {erf}{\left (\frac {\sqrt {2} t}{2} \right )}} \]