67.5.26 problem 6.7 (n)

Internal problem ID [16424]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.7 (n)
Date solved : Thursday, October 02, 2025 at 01:31:24 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Maple. Time used: 0.015 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.666 (sec). Leaf size: 35

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

\begin{align*} y(x)&\to \left (1+e^{c_1}\right ) \left (2 x+1+e^{c_1}\right )\\ y(x)&\to 0\\ y(x)&\to 2 x+1 \end{align*}

✓ Sympy. Time used: 0.463 (sec). Leaf size: 8

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

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