25.6.1 problem 1

Internal problem ID [6885]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 7
Problem number : 1
Date solved : Tuesday, September 30, 2025 at 04:00:03 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-5 y^{\prime }+6&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

ode:=diff(y(x),x)^2-5*diff(y(x),x)+6 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

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

ode=(D[y[x],x])^2-5*D[y[x],x]+6==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.073 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x)**2 - 5*Derivative(y(x), x) + 6,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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