30.6.14 problem 15

Internal problem ID [7549]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Review problems. page 79
Problem number : 15
Date solved : Tuesday, September 30, 2025 at 04:47:11 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=2-\sqrt {2 x -y+3} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 21

ode:=diff(y(x),x) = 2-(2*x-y(x)+3)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ x -2 \sqrt {2 x -y+3}-c_1 = 0 \]

✓ Mathematica. Time used: 0.18 (sec). Leaf size: 54

ode=D[y[x],x] ==2-Sqrt[ 2*x-y[x]+3]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{16} \left (-4 x^2+24 x+4 e^{c_1} (x+1)+44-e^{2 c_1}\right )\\ y(x)&\to \frac {1}{4} \left (-x^2+6 x+11\right ) \end{align*}

✓ Sympy. Time used: 0.460 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(sqrt(2*x - y(x) + 3) + Derivative(y(x), x) - 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 2 x - \frac {\left (C_{1} + x\right )^{2}}{4} + 3 \]