60.1.462 problem 475

Internal problem ID [10476]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 475
Date solved : Sunday, March 30, 2025 at 04:51:14 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} 4 y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.232 (sec). Leaf size: 65

ode:=4*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 &= -\frac {i x}{2} \\ y &= \frac {i x}{2} \\ y &= 0 \\ y &= \sqrt {c_1 \left (c_1 -x \right )} \\ y &= \sqrt {c_1 \left (c_1 +x \right )} \\ y &= -\sqrt {c_1 \left (c_1 -x \right )} \\ y &= -\sqrt {c_1 \left (c_1 +x \right )} \\ \end{align*}

✓ Mathematica. Time used: 0.523 (sec). Leaf size: 140

ode=-y[x] + 2*x*D[y[x],x] + 4*y[x]*D[y[x],x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*Derivative(y(x), x) + 4*y(x)*Derivative(y(x), x)**2 - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out