28.1.124 problem 147

Internal problem ID [4430]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 147
Date solved : Monday, January 27, 2025 at 09:17:03 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} 2 x^{{3}/{2}}+x^{2}+y^{2}+2 y \sqrt {x}\, y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 41

dsolve((2*x*sqrt(x)+x^2+y(x)^2)+(2*y(x)*sqrt(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \sqrt {{\mathrm e}^{-2 \sqrt {x}} c_{1} -x^{2}} \\ y \left (x \right ) &= -\sqrt {{\mathrm e}^{-2 \sqrt {x}} c_{1} -x^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.934 (sec). Leaf size: 55

DSolve[(2*x*Sqrt[x]+x^2+y[x]^2)+(2*y[x]*Sqrt[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {-x^2+c_1 e^{-2 \sqrt {x}}} \\ y(x)\to \sqrt {-x^2+c_1 e^{-2 \sqrt {x}}} \\ \end{align*}