Internal problem ID [14386]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {2 y+\left (2 t +y+1\right ) y^{\prime }=-5 t -1} \]
✓ Solution by Maple
Time used: 0.828 (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)
\[ y \left (t \right ) = \frac {-\sqrt {-\left (t -1\right )^{2} c_{1}^{2}+1}+\left (-2 t -1\right ) c_{1}}{c_{1}} \]
✓ Solution by Mathematica
Time used: 0.228 (sec). Leaf size: 53
DSolve[(5*t+2*y[t]+1)+(2*t+y[t]+1)*y'[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*}