81.1.8 problem 7

Internal problem ID [18532]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter I. Introduction. Exercises at page 13
Problem number : 7
Date solved : Monday, March 31, 2025 at 05:41:31 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.103 (sec). Leaf size: 69

ode:=y(x)-2*x*diff(y(x),x)-y(x)*diff(y(x),x)^2 = 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: 0.453 (sec). Leaf size: 126

ode=y[x]-2*x*D[y[x],x]-y[x]*D[y[x],x]^2==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