57.1.49 problem 49

Internal problem ID [9033]
Book : First order enumerated odes
Section : section 1
Problem number : 49
Date solved : Sunday, March 30, 2025 at 01:59:42 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.026 (sec). Leaf size: 21

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

\begin{align*} y &= \frac {2 x^{{3}/{2}}}{3}+c_1 \\ y &= -\frac {2 x^{{3}/{2}}}{3}+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 33

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

\begin{align*} y(x)\to -\frac {2 x^{3/2}}{3}+c_1 \\ y(x)\to \frac {2 x^{3/2}}{3}+c_1 \\ \end{align*}

✓ Sympy. Time used: 0.352 (sec). Leaf size: 24

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

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