76.3.2 problem 2

Internal problem ID [17302]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.4 (Differences between linear and nonlinear equations). Problems at page 79
Problem number : 2
Date solved : Monday, March 31, 2025 at 03:50:06 PM
CAS classification : [_separable]

\begin{align*} t \left (t -4\right ) y^{\prime }+y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=1 \end{align*}

✓ Maple. Time used: 0.063 (sec). Leaf size: 17

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

\[ y = \frac {\left (\frac {1}{2}+\frac {i}{2}\right ) \sqrt {2}\, t^{{1}/{4}}}{\left (t -4\right )^{{1}/{4}}} \]

✓ Mathematica. Time used: 0.08 (sec). Leaf size: 27

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

\[ y(t)\to \exp \left (\int _2^t\frac {1}{4 K[1]-K[1]^2}dK[1]\right ) \]

✓ Sympy. Time used: 0.279 (sec). Leaf size: 20

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

\[ y{\left (t \right )} = \frac {\sqrt [4]{-1} \sqrt [4]{t}}{\sqrt [4]{t - 4}} \]