10.3.2 problem 2

Internal problem ID [1167]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.4. Page 76
Problem number : 2
Date solved : Monday, January 27, 2025 at 04:39:03 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 20

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

\[ y(t)\to \frac {\sqrt [4]{t}}{\sqrt [4]{4-t}} \]