23.2.322 problem 348

Internal problem ID [5677]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 348
Date solved : Tuesday, September 30, 2025 at 01:49:40 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{4}+4 y {y^{\prime }}^{3}+6 y^{2} {y^{\prime }}^{2}-\left (1-4 y^{3}\right ) y^{\prime }-\left (3-y^{3}\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.048 (sec). Leaf size: 204

ode:=diff(y(x),x)^4+4*y(x)*diff(y(x),x)^3+6*y(x)^2*diff(y(x),x)^2-(1-4*y(x)^3)*diff(y(x),x)-(3-y(x)^3)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ x +\frac {\ln \left (\left (-14640 y^{6}-93435 y^{3}-256\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}+4 y \textit {\_Z}^{3}+6 y^{2} \textit {\_Z}^{2}+\left (4 y^{3}-1\right ) \textit {\_Z} +y^{4}-3 y\right )^{3}+\left (-39648 y^{7}-177915 y^{4}+2048 y\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}+4 y \textit {\_Z}^{3}+6 y^{2} \textit {\_Z}^{2}+\left (4 y^{3}-1\right ) \textit {\_Z} +y^{4}-3 y\right )^{2}+\left (-36144 y^{8}-162033 y^{5}-9216 y^{2}\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}+4 y \textit {\_Z}^{3}+6 y^{2} \textit {\_Z}^{2}+\left (4 y^{3}-1\right ) \textit {\_Z} +y^{4}-3 y\right )-11072 y^{9}-8169 y^{6}+124155 y^{3}\right )}{9}-c_1 = 0 \]

✓ Mathematica. Time used: 81.263 (sec). Leaf size: 2925

ode=(D[y[x],x])^4 +4 y[x] (D[y[x],x])^3+6 y[x]^2 (D[y[x],x])^2-(1-4 y[x]^3) D[y[x],x]- (3-y[x]^3) y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✓ Sympy. Time used: 29.303 (sec). Leaf size: 2825

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((y(x)**3 - 3)*y(x) + (4*y(x)**3 - 1)*Derivative(y(x), x) + 6*y(x)**2*Derivative(y(x), x)**2 + 4*y(x)*Derivative(y(x), x)**3 + Derivative(y(x), x)**4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]