23.2.323 problem 349

Internal problem ID [5678]
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 : 349
Date solved : Tuesday, September 30, 2025 at 01:49:43 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.053 (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 &= -\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 &= \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 &= -\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 &= \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: 86.984 (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]
 

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✓ Sympy. Time used: 24.772 (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)
 

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