90.2.12 problem 12

Internal problem ID [25063]
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 23
Problem number : 12
Date solved : Thursday, October 02, 2025 at 11:48:08 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

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

\[ y = t +1+{\mathrm e}^{t} c_1 \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 14

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

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

✓ Sympy. Time used: 0.071 (sec). Leaf size: 10

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

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