66.7.8 problem 8

Internal problem ID [16036]
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 : 8
Date solved : Thursday, October 02, 2025 at 10:39:23 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\frac {y}{t +1}+4 t^{2}+4 t \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=10 \\ \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 19

ode:=diff(y(t),t) = y(t)/(t+1)+4*t^2+4*t; 
ic:=[y(1) = 10]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 20

ode=D[y[t],t]==y[t]/(1+t)+4*t^2+4*t; 
ic={y[1]==10}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 2 t^3+2 t^2+3 t+3 \end{align*}

✓ Sympy. Time used: 0.156 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-4*t**2 - 4*t + Derivative(y(t), t) - y(t)/(t + 1),0) 
ics = {y(1): 10} 
dsolve(ode,func=y(t),ics=ics)
 

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