83.4.6 problem 6

Internal problem ID [19078]
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 (C) at page 12
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 12:52:14 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: 27

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: 0.354 (sec). Leaf size: 37

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