74.6.53 problem 59 (ii)

Internal problem ID [16076]
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 (ii)
Date solved : Tuesday, January 28, 2025 at 08:36:41 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.148 (sec). Leaf size: 53

dsolve((18/10*t+2*y(t))+(2*t+2*y(t))*diff(y(t),t)=0,y(t), singsol=all)
 

\begin{align*} y &= \frac {-10 c_{1} t -\sqrt {10 c_{1}^{2} t^{2}+10}}{10 c_{1}} \\ y &= \frac {-10 c_{1} t +\sqrt {10 c_{1}^{2} t^{2}+10}}{10 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.523 (sec). Leaf size: 101

DSolve[(18/10*t+2*y[t])+(2*t+2*y[t])*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to -t-\frac {\sqrt {t^2+e^{20 c_1}}}{\sqrt {10}} \\ y(t)\to -t+\frac {\sqrt {t^2+e^{20 c_1}}}{\sqrt {10}} \\ y(t)\to -\frac {\sqrt {t^2}}{\sqrt {10}}-t \\ y(t)\to \frac {\sqrt {t^2}}{\sqrt {10}}-t \\ \end{align*}