74.3.25 problem 20

Internal problem ID [15814]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 20
Date solved : Monday, March 31, 2025 at 01:56:26 PM
CAS classification : [_linear]

\begin{align*} \left (t -2\right ) y^{\prime }+\left (t^{2}-4\right ) y&=\frac {1}{t +2} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.043 (sec). Leaf size: 35

ode:=(t-2)*diff(y(t),t)+(t^2-4)*y(t) = 1/(t+2); 
ic:=y(0) = 3; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \left (\int _{0}^{t}\frac {{\mathrm e}^{\frac {\textit {\_z1} \left (\textit {\_z1} +4\right )}{2}}}{\textit {\_z1}^{2}-4}d \textit {\_z1} +3\right ) {\mathrm e}^{-\frac {t \left (t +4\right )}{2}} \]

✓ Mathematica. Time used: 0.269 (sec). Leaf size: 46

ode=(t-2)*D[y[t],t]+(t^2-4)*y[t]==1/(t+2); 
ic={y[0]==3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-\frac {1}{2} t (t+4)} \left (\int _0^t\frac {e^{\frac {1}{2} K[1] (K[1]+4)}}{K[1]^2-4}dK[1]+3\right ) \]

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((t - 2)*Derivative(y(t), t) + (t**2 - 4)*y(t) - 1/(t + 2),0) 
ics = {y(0): 3} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out