90.4.13 problem 14

Internal problem ID [25108]
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 59
Problem number : 14
Date solved : Thursday, October 02, 2025 at 11:50:24 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

\[ y = \left (t +c_1 \right ) \left (t +1\right )^{2} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 15

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

\begin{align*} y(t)&\to (t+1)^2 (t+c_1) \end{align*}

✓ Sympy. Time used: 0.197 (sec). Leaf size: 24

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

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