47.1.32 problem 32

Internal problem ID [7413]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page 7
Problem number : 32
Date solved : Wednesday, March 05, 2025 at 04:27:14 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=2 \sqrt {2 x +y+1} \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 56

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

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

✓ Mathematica. Time used: 9.064 (sec). Leaf size: 48

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

\begin{align*} y(x)\to W\left (-e^{-x-\frac {3}{2}+c_1}\right ){}^2+2 W\left (-e^{-x-\frac {3}{2}+c_1}\right )-2 x \\ y(x)\to -2 x \\ \end{align*}

✓ Sympy. Time used: 1.059 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = - 2 x + \left (W\left (C_{1} e^{- x - 1}\right ) + 1\right )^{2} - 1 \]