85.8.1 problem 1

Internal problem ID [22471]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. C Exercises at page 33
Problem number : 1
Date solved : Thursday, October 02, 2025 at 08:40:26 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.186 (sec). Leaf size: 57

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

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

✓ Sympy. Time used: 0.424 (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)
 

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