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 : Tuesday, February 04, 2025 at 12:22:39 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 29

dsolve((sqrt(x)+x)*diff(y(x),x)=sqrt(y(x))+y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[(Sqrt[x]+x)*D[y[x],x]==Sqrt[y[x]]+y[x],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*}