72.7.3 problem 3

Internal problem ID [14673]
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 : 3
Date solved : Monday, March 31, 2025 at 12:52:23 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 26

ode:=diff(y(t),t) = -y(t)/(t+1)+t^2; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {3 t^{4}+4 t^{3}+12 c_1}{12+12 t} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 28

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

\[ y(t)\to \frac {3 t^4+4 t^3+12 c_1}{12 t+12} \]

✓ Sympy. Time used: 0.236 (sec). Leaf size: 17

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

\[ y{\left (t \right )} = \frac {C_{1} + \frac {t^{4}}{4} + \frac {t^{3}}{3}}{t + 1} \]