74.6.32 problem 33

Internal problem ID [15984]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 33
Date solved : Monday, March 31, 2025 at 02:20:42 PM
CAS classification : [_linear]

\begin{align*} 2 t y+3 t^{2}+\left (t^{2}-1\right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.242 (sec). Leaf size: 14

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

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