Internal problem ID [14393]
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: 53.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {y^{\prime } t -y-{y^{\prime }}^{2}+y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 28
dsolve(t*diff(y(t),t)-y(t)-1=diff(y(t),t)^2-diff(y(t),t),y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {1}{4} t^{2}+\frac {1}{2} t -\frac {3}{4} \\ y \left (t \right ) &= -c_{1}^{2}+c_{1} t +c_{1} -1 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 35
DSolve[t*y'[t]-y[t]-1==y'[t]^2-y'[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_1 (t+1)-1-c_1{}^2 \\ y(t)\to \frac {1}{4} \left (t^2+2 t-3\right ) \\ \end{align*}