30.5.17 problem 17

Internal problem ID [7516]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.6, Substitutions and Transformations. Exercises. page 76
Problem number : 17
Date solved : Tuesday, September 30, 2025 at 04:41:40 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 16

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

\[ x -2 \sqrt {x +y}-c_1 = 0 \]

✓ Mathematica. Time used: 0.081 (sec). Leaf size: 24

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

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

✓ Sympy. Time used: 0.412 (sec). Leaf size: 10

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

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