15.20.1 problem 1

Internal problem ID [3309]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 38, page 173
Problem number : 1
Date solved : Sunday, March 30, 2025 at 01:34:33 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.029 (sec). Leaf size: 40

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

\begin{align*} y &= \frac {\left (-1-4 x \right ) \sqrt {1+4 x}}{12}-\frac {x}{2}+c_1 \\ y &= -\frac {x}{2}+\frac {\left (1+4 x \right )^{{3}/{2}}}{12}+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 54

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

\begin{align*} y(x)\to \frac {1}{2} \left (-\frac {1}{6} (4 x+1)^{3/2}-x\right )+c_1 \\ y(x)\to \frac {1}{12} \left ((4 x+1)^{3/2}-6 x+12 c_1\right ) \\ \end{align*}

✓ Sympy. Time used: 0.237 (sec). Leaf size: 34

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

\[ \left [ y{\left (x \right )} = C_{1} - \frac {x}{2} - \frac {\left (4 x + 1\right )^{\frac {3}{2}}}{12}, \ y{\left (x \right )} = C_{1} - \frac {x}{2} + \frac {\left (4 x + 1\right )^{\frac {3}{2}}}{12}\right ] \]