90.7.18 problem 19 (a)

Internal problem ID [25172]
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 99
Problem number : 19 (a)
Date solved : Thursday, October 02, 2025 at 11:57:28 PM
CAS classification : [_linear]

\begin{align*} t y^{\prime }&=2 y-t \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 11

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

\[ y = c_1 \,t^{2}+t \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 22

ode=D[y[t],t]== 2*y[t]-t; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {t}{2}+c_1 e^{2 t}+\frac {1}{4} \end{align*}

✓ Sympy. Time used: 0.066 (sec). Leaf size: 15

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

\[ y{\left (t \right )} = C_{1} e^{2 t} + \frac {t}{2} + \frac {1}{4} \]