74.6.54 problem 59 (iii)

Internal problem ID [16077]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 59 (iii)
Date solved : Tuesday, January 28, 2025 at 08:36:47 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.142 (sec). Leaf size: 53

dsolve((2*t+19/10*y(t))+(19/10*t+2*y(t))*diff(y(t),t)=0,y(t), singsol=all)
 

\begin{align*} y &= \frac {-19 c_{1} t -\sqrt {-39 c_{1}^{2} t^{2}+40}}{20 c_{1}} \\ y &= \frac {-19 c_{1} t +\sqrt {-39 c_{1}^{2} t^{2}+40}}{20 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.440 (sec). Leaf size: 114

DSolve[(2*t+19/10*y[t])+(19/10*t+2*y[t])*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {1}{20} \left (-19 t-\sqrt {-39 t^2+40 e^{c_1}}\right ) \\ y(t)\to \frac {1}{20} \left (-19 t+\sqrt {-39 t^2+40 e^{c_1}}\right ) \\ y(t)\to \frac {1}{20} \left (-\sqrt {39} \sqrt {-t^2}-19 t\right ) \\ y(t)\to \frac {1}{20} \left (\sqrt {39} \sqrt {-t^2}-19 t\right ) \\ \end{align*}