47.2.27 problem 27

Internal problem ID [7443]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 27
Date solved : Sunday, March 30, 2025 at 12:06:51 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.174 (sec). Leaf size: 69

ode:=y(x)*diff(y(x),x)^2+2*x*diff(y(x),x)-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -i x \\ y &= i x \\ y &= 0 \\ y &= \sqrt {c_1 \left (c_1 -2 x \right )} \\ y &= \sqrt {c_1 \left (c_1 +2 x \right )} \\ y &= -\sqrt {c_1 \left (c_1 -2 x \right )} \\ y &= -\sqrt {c_1 \left (c_1 +2 x \right )} \\ \end{align*}

✓ Mathematica. Time used: 0.476 (sec). Leaf size: 126

ode=y[x]*(D[y[x],x])^2+2*x*D[y[x],x]-y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -e^{\frac {c_1}{2}} \sqrt {-2 x+e^{c_1}} \\ y(x)\to e^{\frac {c_1}{2}} \sqrt {-2 x+e^{c_1}} \\ y(x)\to -e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ y(x)\to e^{\frac {c_1}{2}} \sqrt {2 x+e^{c_1}} \\ y(x)\to 0 \\ y(x)\to -i x \\ y(x)\to i x \\ \end{align*}

✗ Sympy

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

Timed Out