62.17.5 problem Ex 5

Internal problem ID [12834]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IV, differential equations of the first order and higher degree than the first. Article 28. Summary. Page 59
Problem number : Ex 5
Date solved : Monday, March 31, 2025 at 07:20:34 AM
CAS classification : [[_homogeneous, `class C`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.034 (sec). Leaf size: 53

ode:=y(x) = diff(y(x),x)^2*(1+x); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= \frac {\left (x +1+\sqrt {\left (x +1\right ) \left (1+c_1 \right )}\right )^{2}}{x +1} \\ y &= \frac {\left (-x -1+\sqrt {\left (x +1\right ) \left (1+c_1 \right )}\right )^{2}}{x +1} \\ \end{align*}

✓ Mathematica. Time used: 0.067 (sec). Leaf size: 57

ode=y[x]==(D[y[x],x])^2*(x+1); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to x-c_1 \sqrt {x+1}+1+\frac {c_1{}^2}{4} \\ y(x)\to x+c_1 \sqrt {x+1}+1+\frac {c_1{}^2}{4} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.868 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(x + 1)*Derivative(y(x), x)**2 + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}^{2}}{4} - C_{1} \sqrt {x + 1} + x + 1 \]