Internal problem ID [14392]
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: 52.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]
\[ \boxed {y^{\prime } t -y-2 \left (y^{\prime } t -y\right )^{2}-y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.079 (sec). Leaf size: 53
dsolve(t*diff(y(t),t)-y(t)-2*(t*diff(y(t),t)-y(t))^2=diff(y(t),t)+1,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {-7 t^{2}-2 t +1}{8 t} \\ y \left (t \right ) &= c_{1} t -\frac {1}{4}-\frac {\sqrt {-8 c_{1} -7}}{4} \\ y \left (t \right ) &= c_{1} t -\frac {1}{4}+\frac {\sqrt {-8 c_{1} -7}}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.048 (sec). Leaf size: 90
DSolve[t*y'[t]-y[t]-2*(t*y'[t]-y[t])^2==y'[t]+1,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{8} \left (-7 t-e^{-2 c_1} t-2+2 e^{-c_1}\right ) \\ y(t)\to \frac {1}{8} \left (-7 t-e^{-2 c_1} t-2-2 e^{-c_1}\right ) \\ y(t)\to \frac {1}{8} (-7 t-2) \\ y(t)\to \frac {1}{8} \left (-7 t+\frac {1}{t}-2\right ) \\ \end{align*}