76.3.2 problem 2

Internal problem ID [17373]
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 : Tuesday, January 28, 2025 at 10:03:26 AM
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*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.080 (sec). Leaf size: 27

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

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