15.8.46 problem 49

Internal problem ID [3049]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 49
Date solved : Monday, January 27, 2025 at 07:11:49 AM
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 (2\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.056 (sec). Leaf size: 23

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

\begin{align*} y &= \sqrt {x \left (x -2\right )} \\ y &= -\sqrt {x \left (x -2\right )} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.198 (sec). Leaf size: 36

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

\begin{align*} y(x)\to -\sqrt {x-2} \sqrt {x} \\ y(x)\to \sqrt {x-2} \sqrt {x} \\ \end{align*}