72.2.8 problem 8

Internal problem ID [14564]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.3 page 47
Problem number : 8
Date solved : Thursday, March 13, 2025 at 03:34:22 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 15

ode:=diff(y(t),t) = 2*y(t)-t; 
ic:=y(0) = 1/2; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \frac {t}{2}+\frac {1}{4}+\frac {{\mathrm e}^{2 t}}{4} \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 35

ode=D[y[t],t]==2*y[t]-t; 
ic={y[0]==1/2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {1}{2} e^{2 t} \left (2 \int _0^t-e^{-2 K[1]} K[1]dK[1]+1\right ) \]

✓ Sympy. Time used: 0.137 (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 = {y(0): 1/2} 
dsolve(ode,func=y(t),ics=ics)
 

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