29.25.12 problem 709

Internal problem ID [5299]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 709
Date solved : Sunday, March 30, 2025 at 07:52:06 AM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} 2 \left (x -y^{4}\right ) y^{\prime }&=y \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 89

ode:=2*(x-y(x)^4)*diff(y(x),x) = y(x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {\sqrt {-2 \sqrt {c_1^{2}-4 x}+2 c_1}}{2} \\ y &= \frac {\sqrt {-2 \sqrt {c_1^{2}-4 x}+2 c_1}}{2} \\ y &= -\frac {\sqrt {2 \sqrt {c_1^{2}-4 x}+2 c_1}}{2} \\ y &= \frac {\sqrt {2 \sqrt {c_1^{2}-4 x}+2 c_1}}{2} \\ \end{align*}

✓ Mathematica. Time used: 2.15 (sec). Leaf size: 128

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

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

✓ Sympy. Time used: 4.557 (sec). Leaf size: 102

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

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {2} \sqrt {- C_{1} - \sqrt {C_{1}^{2} - 4 x}}}{2}, \ y{\left (x \right )} = \frac {\sqrt {2} \sqrt {- C_{1} - \sqrt {C_{1}^{2} - 4 x}}}{2}, \ y{\left (x \right )} = - \frac {\sqrt {2} \sqrt {- C_{1} + \sqrt {C_{1}^{2} - 4 x}}}{2}, \ y{\left (x \right )} = \frac {\sqrt {2} \sqrt {- C_{1} + \sqrt {C_{1}^{2} - 4 x}}}{2}\right ] \]