83.7.5 problem 4 (a)

Internal problem ID [19123]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (F) at page 24
Problem number : 4 (a)
Date solved : Tuesday, January 28, 2025 at 12:58:39 PM
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 \left (x \right ) &= \sqrt {\left (x +c_{1} \right ) x} \\ y \left (x \right ) &= -\sqrt {\left (x +c_{1} \right ) x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.192 (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*}