90.7.19 problem 19 (b)

Internal problem ID [25173]
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 (b)
Date solved : Thursday, October 02, 2025 at 11:57:30 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ \end{align*}

✗ Maple

ode:=t*diff(y(t),t) = 2*y(t)-t; 
ic:=[y(0) = 2]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 21

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

\begin{align*} y(t)&\to \frac {1}{4} \left (2 t+7 e^{2 t}+1\right ) \end{align*}

✓ Sympy. Time used: 0.075 (sec). Leaf size: 17

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

\[ y{\left (t \right )} = \frac {t}{2} + \frac {7 e^{2 t}}{4} + \frac {1}{4} \]