47.1.10 problem 10

Internal problem ID [7391]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page 7
Problem number : 10
Date solved : Monday, January 27, 2025 at 02:51:50 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 29

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

\begin{align*} y &= \sqrt {{\mathrm e}^{\frac {1}{x}} c_{1} +2} \\ y &= -\sqrt {{\mathrm e}^{\frac {1}{x}} c_{1} +2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.307 (sec). Leaf size: 70

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

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