74.7.50 problem 53

Internal problem ID [16127]
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
Date solved : Tuesday, January 28, 2025 at 08:50:19 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y^{\prime } t -y-1&={y^{\prime }}^{2}-y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.063 (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 &= \frac {1}{4} t^{2}+\frac {1}{2} t -\frac {3}{4} \\ y &= -c_{1}^{2}+c_{1} t +c_{1} -1 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 35

DSolve[t*D[y[t],t]-y[t]-1==D[y[t],t]^2-D[y[t],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*}