74.7.58 problem 65

Internal problem ID [16135]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 65
Date solved : Tuesday, January 28, 2025 at 08:51:14 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} y^{\prime }&=\frac {y^{2}-t^{2}}{t y} \end{align*}

With initial conditions

\begin{align*} y \left (4\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.177 (sec). Leaf size: 34

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

\begin{align*} y &= \sqrt {-2 \ln \left (t \right )+4 \ln \left (2\right )}\, t \\ y &= -\sqrt {-2 \ln \left (t \right )+4 \ln \left (2\right )}\, t \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.179 (sec). Leaf size: 36

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

\begin{align*} y(t)\to -t \sqrt {\log (16)-2 \log (t)} \\ y(t)\to t \sqrt {\log (16)-2 \log (t)} \\ \end{align*}