Internal problem ID [14395]
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: 55.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {-2 y^{\prime } t +2 y-\frac {1}{{y^{\prime }}^{2}}=-1} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 62
dsolve(1-2*(t*diff(y(t),t)-y(t))=1/diff(y(t),t)^2,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \frac {3 t^{\frac {2}{3}}}{2}-\frac {1}{2} \\ y \left (t \right ) &= -\frac {3 t^{\frac {2}{3}}}{4}-\frac {3 i \sqrt {3}\, t^{\frac {2}{3}}}{4}-\frac {1}{2} \\ y \left (t \right ) &= -\frac {3 t^{\frac {2}{3}}}{4}+\frac {3 i \sqrt {3}\, t^{\frac {2}{3}}}{4}-\frac {1}{2} \\ y \left (t \right ) &= -\frac {1}{2}+c_{1} t +\frac {1}{2 c_{1}^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 93
DSolve[1-2*(t*y'[t]-y[t])==1/y'[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} \left (2 c_1 t-1+\frac {1}{c_1{}^2}\right ) \\ y(t)\to \frac {1}{2} \left (3 t^{2/3}-1\right ) \\ y(t)\to -\frac {1}{2}+\frac {3}{4} i \left (\sqrt {3}+i\right ) t^{2/3} \\ y(t)\to -\frac {1}{2}-\frac {3}{4} \left (1+i \sqrt {3}\right ) t^{2/3} \\ \end{align*}