83.21.10 problem 10

Internal problem ID [19183]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (D) at page 57
Problem number : 10
Date solved : Monday, March 31, 2025 at 06:51:29 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: 0.059 (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: 0.513 (sec). Leaf size: 140

ode=4*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 -\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