23.2.265 problem 280

Internal problem ID [5620]
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 : 280
Date solved : Tuesday, September 30, 2025 at 01:13:26 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{3}-7 y^{\prime }+6&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=diff(y(x),x)^3-7*diff(y(x),x)+6 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 2 x +c_1 \\ y &= x +c_1 \\ y &= -3 x +c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 29

ode=(D[y[x],x])^3-7 D[y[x],x]+6==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -3 x+c_1\\ y(x)&\to x+c_1\\ y(x)&\to 2 x+c_1 \end{align*}

✓ Sympy. Time used: 0.084 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x)**3 - 7*Derivative(y(x), x) + 6,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} + x, \ y{\left (x \right )} = C_{1} + 2 x, \ y{\left (x \right )} = C_{1} - 3 x\right ] \]