77.43.4 problem Ex 5 page 7

Internal problem ID [20796]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter II. Equations of first order and first degree
Problem number : Ex 5 page 7
Date solved : Thursday, October 02, 2025 at 06:23:29 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \left (x +2 y^{3}\right ) y^{\prime }&=y \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 224

ode:=(x+2*y(x)^3)*diff(y(x),x) = y(x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {\left (108 x +12 \sqrt {12 c_1^{3}+81 x^{2}}\right )^{{2}/{3}}-12 c_1}{6 \left (108 x +12 \sqrt {12 c_1^{3}+81 x^{2}}\right )^{{1}/{3}}} \\ y &= -\frac {i \left (108 x +12 \sqrt {12 c_1^{3}+81 x^{2}}\right )^{{2}/{3}} \sqrt {3}+12 i \sqrt {3}\, c_1 +\left (108 x +12 \sqrt {12 c_1^{3}+81 x^{2}}\right )^{{2}/{3}}-12 c_1}{12 \left (108 x +12 \sqrt {12 c_1^{3}+81 x^{2}}\right )^{{1}/{3}}} \\ y &= \frac {i \left (108 x +12 \sqrt {12 c_1^{3}+81 x^{2}}\right )^{{2}/{3}} \sqrt {3}+12 i \sqrt {3}\, c_1 -\left (108 x +12 \sqrt {12 c_1^{3}+81 x^{2}}\right )^{{2}/{3}}+12 c_1}{12 \left (108 x +12 \sqrt {12 c_1^{3}+81 x^{2}}\right )^{{1}/{3}}} \\ \end{align*}

✓ Mathematica. Time used: 1.153 (sec). Leaf size: 285

ode=(x+2*y[x]^3)*D[y[x],x]==y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2 \sqrt [3]{3} c_1-\sqrt [3]{2} \left (-9 x+\sqrt {81 x^2+12 c_1{}^3}\right ){}^{2/3}}{6^{2/3} \sqrt [3]{-9 x+\sqrt {81 x^2+12 c_1{}^3}}}\\ y(x)&\to \frac {2^{2/3} \sqrt [3]{3} \left (1-i \sqrt {3}\right ) \left (-9 x+\sqrt {81 x^2+12 c_1{}^3}\right ){}^{2/3}-2 \sqrt [3]{2} \sqrt [6]{3} \left (\sqrt {3}+3 i\right ) c_1}{12 \sqrt [3]{-9 x+\sqrt {81 x^2+12 c_1{}^3}}}\\ y(x)&\to \frac {2^{2/3} \sqrt [3]{3} \left (1+i \sqrt {3}\right ) \left (-9 x+\sqrt {81 x^2+12 c_1{}^3}\right ){}^{2/3}-2 \sqrt [3]{2} \sqrt [6]{3} \left (\sqrt {3}-3 i\right ) c_1}{12 \sqrt [3]{-9 x+\sqrt {81 x^2+12 c_1{}^3}}}\\ y(x)&\to 0 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 2*y(x)**3)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out