Internal problem ID [14431]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Review exercises, page 80
Problem number: 29.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {y-y^{\prime } t +4 {y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 19
dsolve(y(t)-t*diff(y(t),t)=-4*diff(y(t),t)^2,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {t^{2}}{16} \\ y \left (t \right ) &= c_{1} \left (-4 c_{1} +t \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 25
DSolve[y[t]-t*y'[t]==-4*y'[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_1 (t-4 c_1) \\ y(t)\to \frac {t^2}{16} \\ \end{align*}