82.13.6 problem Ex. 6

Internal problem ID [18735]
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. Problems at page 32
Problem number : Ex. 6
Date solved : Monday, March 31, 2025 at 06:03:33 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-7 y^{\prime }+12&=0 \end{align*}

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

ode:=diff(y(x),x)^2-7*diff(y(x),x)+12 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 4 x +c_1 \\ y &= 3 x +c_1 \\ \end{align*}

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

ode=D[y[x],x]^2-7*D[y[x],x]+12==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to 3 x+c_1 \\ y(x)\to 4 x+c_1 \\ \end{align*}

✓ Sympy. Time used: 0.124 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x)**2 - 7*Derivative(y(x), x) + 12,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} + 4 x, \ y{\left (x \right )} = C_{1} + 3 x\right ] \]