23.1.418 problem 407

Internal problem ID [5025]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 407
Date solved : Tuesday, September 30, 2025 at 11:27:21 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime } \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}&=0 \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 5

ode:=diff(y(x),x)*(a__4*x^4+a__3*x^3+a__2*x^2+a__1*x+a__0)^(1/2) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 7

ode=D[y[x],x]*Sqrt[a0+a1*x+a2*x^2+a3*x^3+a4*x^4]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \end{align*}

✓ Sympy. Time used: 0.023 (sec). Leaf size: 3

from sympy import * 
x = symbols("x") 
a0 = symbols("a0") 
a1 = symbols("a1") 
a2 = symbols("a2") 
a3 = symbols("a3") 
a4 = symbols("a4") 
y = Function("y") 
ode = Eq(sqrt(a0 + a1*x + a2*x**2 + a3*x**3 + a4*x**4)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \]