32.1.11 problem First order with homogeneous Coefficients. Exercise 7.12, page 61

Internal problem ID [5781]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 7
Problem number : First order with homogeneous Coefficients. Exercise 7.12, page 61
Date solved : Monday, January 27, 2025 at 01:17:30 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (-1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.059 (sec). Leaf size: 23

dsolve([(x^2+y(x)^2)=2*x*y(x)*diff(y(x),x),y(-1) = 0],y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \sqrt {x \left (x +1\right )} \\ y \left (x \right ) &= -\sqrt {x \left (x +1\right )} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.202 (sec). Leaf size: 36

DSolve[{(x^2+y[x]^2)==2*x*y[x]*D[y[x],x],y[-1]==0},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {x} \sqrt {x+1} \\ y(x)\to \sqrt {x} \sqrt {x+1} \\ \end{align*}