29.36.25 problem 1094

Internal problem ID [5652]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 36
Problem number : 1094
Date solved : Tuesday, March 04, 2025 at 11:16:32 PM
CAS classification : [_quadrature]

\begin{align*} 2 {y^{\prime }}^{4}-y y^{\prime }-2&=0 \end{align*}

✓ Maple. Time used: 0.076 (sec). Leaf size: 217

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

\begin{align*} y \left (x \right ) &= -\frac {\sqrt {-6 \sqrt {\left (c_{1}^{2}-2 c_{1} x +x^{2}+12\right )^{3}}-6 c_{1}^{3}+18 c_{1}^{2} x +\left (-18 x^{2}+216\right ) c_{1} +6 x^{3}-216 x}}{9} \\ y \left (x \right ) &= \frac {\sqrt {-6 \sqrt {\left (c_{1}^{2}-2 c_{1} x +x^{2}+12\right )^{3}}-6 c_{1}^{3}+18 c_{1}^{2} x +\left (-18 x^{2}+216\right ) c_{1} +6 x^{3}-216 x}}{9} \\ y \left (x \right ) &= -\frac {\sqrt {6 \sqrt {\left (c_{1}^{2}-2 c_{1} x +x^{2}+12\right )^{3}}-6 c_{1}^{3}+18 c_{1}^{2} x +\left (-18 x^{2}+216\right ) c_{1} +6 x^{3}-216 x}}{9} \\ y \left (x \right ) &= \frac {\sqrt {6 \sqrt {\left (c_{1}^{2}-2 c_{1} x +x^{2}+12\right )^{3}}-6 c_{1}^{3}+18 c_{1}^{2} x +\left (-18 x^{2}+216\right ) c_{1} +6 x^{3}-216 x}}{9} \\ \end{align*}

✓ Mathematica. Time used: 113.923 (sec). Leaf size: 12753

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

Too large to display

✓ Sympy. Time used: 40.784 (sec). Leaf size: 806

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

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