83.4.20 problem 20

Internal problem ID [19092]
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 : 20
Date solved : Tuesday, January 28, 2025 at 12:55:40 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x^{2}+3 y^{2}-2 x y y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 26

dsolve((x^2+3*y(x)^2)-2*x*y(x)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.286 (sec). Leaf size: 34

DSolve[(x^2+3*y[x]^2)-2*x*y[x]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x \sqrt {-1+c_1 x} \\ y(x)\to x \sqrt {-1+c_1 x} \\ \end{align*}