44.5.61 problem 51

Internal problem ID [7123]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 51
Date solved : Sunday, March 30, 2025 at 11:43:23 AM
CAS classification : [_separable]

\begin{align*} \left (\sqrt {x}+x \right ) y^{\prime }&=\sqrt {y}+y \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

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

\[ -\frac {\sqrt {x -1}\, \left (\sqrt {x}+1\right ) c_1}{\sqrt {1-x}}+\sqrt {y}+1 = 0 \]

✓ Mathematica. Time used: 3.421 (sec). Leaf size: 35

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

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

✓ Sympy. Time used: 0.592 (sec). Leaf size: 31

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

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