60.1.451 problem 464

Internal problem ID [10465]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 464
Date solved : Sunday, March 30, 2025 at 04:50:43 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: 0.235 (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: 0.456 (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