85.30.2 problem 2

Internal problem ID [22618]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 63
Problem number : 2
Date solved : Thursday, October 02, 2025 at 08:55:09 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y&=x y^{\prime }+1+4 {y^{\prime }}^{2} \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 24

ode:=y(x) = x*diff(y(x),x)+1+4*diff(y(x),x)^2; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {x^{2}}{16}+1 \\ y &= 4 c_1^{2}+c_1 x +1 \\ \end{align*}

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 30

ode=y[x]==x*D[y[x],{x,1}]+1+4*D[y[x],{x,1}]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 x+1+4 c_1{}^2\\ y(x)&\to 1-\frac {x^2}{16} \end{align*}

✓ Sympy. Time used: 1.052 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*Derivative(y(x), x) + y(x) - 4*Derivative(y(x), x)**2 - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}^{2}}{16} + \frac {C_{1} x}{8} + 1 \]