74.8.29 problem 29

Internal problem ID [16094]
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 : Monday, March 31, 2025 at 02:41:43 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Maple. Time used: 0.029 (sec). Leaf size: 19

ode:=y(t)-t*diff(y(t),t) = -4*diff(y(t),t)^2; 
dsolve(ode,y(t), singsol=all);
 

\begin{align*} y &= \frac {t^{2}}{16} \\ y &= c_1 \left (-4 c_1 +t \right ) \\ \end{align*}

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

ode=y[t]-t*D[y[t],t]==-4*D[y[t],t]^2; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 1.766 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t*Derivative(y(t), t) + y(t) + 4*Derivative(y(t), t)**2,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {t^{2}}{16} - \frac {\left (C_{1} + t\right )^{2}}{16} \]