7.5.16 problem 16

Internal problem ID [120]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 16
Date solved : Saturday, March 29, 2025 at 04:33:20 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\sqrt {x +y+1} \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 44

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

\[ x -2 \sqrt {x +y+1}-\ln \left (-1+\sqrt {x +y+1}\right )+\ln \left (1+\sqrt {x +y+1}\right )+\ln \left (y+x \right )-c_1 = 0 \]

✓ Mathematica. Time used: 8.951 (sec). Leaf size: 56

ode=D[y[x],x]==Sqrt[x+y[x]+1]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to W\left (-e^{-\frac {x}{2}-1-\frac {c_1}{2}}\right ){}^2+2 W\left (-e^{-\frac {x}{2}-1-\frac {c_1}{2}}\right )-x \\ y(x)\to -x \\ \end{align*}

✓ Sympy. Time used: 0.840 (sec). Leaf size: 31

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

\[ C_{1} + x - 2 \sqrt {x + y{\left (x \right )} + 1} + 2 \log {\left (\sqrt {x + y{\left (x \right )} + 1} + 1 \right )} = 0 \]