29.36.24 problem 1093

Internal problem ID [5651]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 36
Problem number : 1093
Date solved : Tuesday, March 04, 2025 at 11:16:25 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: 0.052 (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);
 

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

✓ Mathematica. Time used: 92.672 (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: 51.248 (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)
 

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