82.16.2 problem Ex. 2

Internal problem ID [18737]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter III. Equations of the first order but not of the first degree. Problems at page 36
Problem number : Ex. 2
Date solved : Thursday, March 13, 2025 at 12:44:47 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.038 (sec). Leaf size: 69

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

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

✓ Mathematica. Time used: 0.434 (sec). Leaf size: 126

ode=y[x]==y[x]*D[y[x],x]^2+2*D[y[x],x]*x; 
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