62.9.4 problem Ex 4

Internal problem ID [12835]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 16. Integrating factors by inspection. Page 23
Problem number : Ex 4
Date solved : Tuesday, January 28, 2025 at 04:26:08 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x^{2}+y^{2}-2 x y y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.200 (sec). Leaf size: 38

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

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