76.18.5 problem Ex. 5

Internal problem ID [20112]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter III. Equations of the first order but not of the first degree. Examples on chapter III. page 38
Problem number : Ex. 5
Date solved : Thursday, October 02, 2025 at 05:26:00 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-9 y^{\prime }+18&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=diff(y(x),x)^2-9*diff(y(x),x)+18 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 6 x +c_1 \\ y &= 3 x +c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 21

ode=D[y[x],x]^2-9*D[y[x],x]+18==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3 x+c_1\\ y(x)&\to 6 x+c_1 \end{align*}

✓ Sympy. Time used: 0.075 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x)**2 - 9*Derivative(y(x), x) + 18,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} + 6 x, \ y{\left (x \right )} = C_{1} + 3 x\right ] \]