29.29.21 problem 843

Internal problem ID [5426]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 29
Problem number : 843
Date solved : Sunday, March 30, 2025 at 08:12:51 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.029 (sec). Leaf size: 25

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

\begin{align*} y &= 2 \sqrt {x a}+c_1 \\ y &= -2 \sqrt {x a}+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 39

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

\begin{align*} y(x)\to -2 \sqrt {a} \sqrt {x}+c_1 \\ y(x)\to 2 \sqrt {a} \sqrt {x}+c_1 \\ \end{align*}

✓ Sympy. Time used: 0.431 (sec). Leaf size: 31

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

\[ \left [ y{\left (x \right )} = C_{1} - 2 \sqrt {a} \sqrt {x}, \ y{\left (x \right )} = C_{1} + 2 \sqrt {a} \sqrt {x}\right ] \]