16.1.13 problem 3(g)

Internal problem ID [3415]
Book : Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
Section : Exercis 2, page 5
Problem number : 3(g)
Date solved : Tuesday, March 04, 2025 at 04:38:10 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-3 y^{\prime }+2&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=diff(y(x),x)^2-3*diff(y(x),x)+2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y \left (x \right ) &= 2 x +c_{1} \\ y \left (x \right ) &= x +c_{1} \\ \end{align*}

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 19

ode=(D[y[x],x])^2-3*D[y[x],x]+2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.118 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x)**2 - 3*Derivative(y(x), x) + 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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