Internal problem ID [14343]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime }=-2 t} \]
✓ Solution by Maple
Time used: 0.094 (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 \left (t \right ) &= \frac {-19 c_{1} t -\sqrt {-39 c_{1}^{2} t^{2}+40}}{20 c_{1}} \\ y \left (t \right ) &= \frac {-19 c_{1} t +\sqrt {-39 c_{1}^{2} t^{2}+40}}{20 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.461 (sec). Leaf size: 114
DSolve[(2*t+19/10*y[t])+(19/10*t+2*y[t])*y'[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*}