29.26.13 problem 749

Internal problem ID [5334]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 749
Date solved : Tuesday, March 04, 2025 at 09:29:35 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.035 (sec). Leaf size: 17

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

\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\left (-c_{1} +x \right )^{2}}{4} \\ \end{align*}

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 36

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

\begin{align*} y(x)\to \frac {1}{4} (x-c_1){}^2 \\ y(x)\to \frac {1}{4} (x+c_1){}^2 \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.285 (sec). Leaf size: 17

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

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