72.7.7 problem 7

Internal problem ID [14677]
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 1.9 page 133
Problem number : 7
Date solved : Monday, March 31, 2025 at 12:52:33 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=-\frac {y}{1+t}+2 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3 \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 18

ode:=diff(y(t),t) = -y(t)/(t+1)+2; 
ic:=y(0) = 3; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \frac {t^{2}+2 t +3}{1+t} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 19

ode=D[y[t],t]==-y[t]/(1+t)+2; 
ic={y[0]==3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {t^2+2 t+3}{t+1} \]

✓ Sympy. Time used: 0.220 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), t) - 2 + y(t)/(t + 1),0) 
ics = {y(0): 3} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {t^{2} + 2 t + 3}{t + 1} \]