74.8.29 problem 29

Internal problem ID [16165]
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
Date solved : Tuesday, January 28, 2025 at 08:53:20 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y-y^{\prime } t&=-4 {y^{\prime }}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.092 (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 &= \frac {t^{2}}{16} \\ y &= c_{1} \left (-4 c_{1} +t \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 25

DSolve[y[t]-t*D[y[t],t]==-4*D[y[t],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*}