74.7.43 problem 42 (b)

Internal problem ID [16120]
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 : 42 (b)
Date solved : Tuesday, January 28, 2025 at 08:50:03 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 1.621 (sec). Leaf size: 32

dsolve((5*t+2*y(t)+1)+(2*t+y(t)+1)*diff(y(t),t)=0,y(t), singsol=all)
 

\[ y = \frac {-\sqrt {-\left (t -1\right )^{2} c_{1}^{2}+1}+\left (-2 t -1\right ) c_{1}}{c_{1}} \]

✓ Solution by Mathematica

Time used: 0.155 (sec). Leaf size: 53

DSolve[(5*t+2*y[t]+1)+(2*t+y[t]+1)*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to -\sqrt {-t^2+2 t+1+c_1}-2 t-1 \\ y(t)\to \sqrt {-t^2+2 t+1+c_1}-2 t-1 \\ \end{align*}