56.1.44 problem 44

Internal problem ID [8756]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 44
Date solved : Wednesday, March 05, 2025 at 06:45:52 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.035 (sec). Leaf size: 39

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

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

✓ Mathematica. Time used: 0.052 (sec). Leaf size: 46

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

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

✓ Sympy. Time used: 0.693 (sec). Leaf size: 15

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

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