40.3.21 problem 25 (f)

Internal problem ID [6625]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 25 (f)
Date solved : Monday, January 27, 2025 at 02:16:16 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

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

\begin{align*} y &= \sqrt {\left (3 x +c_1 \right ) x} \\ y &= -\sqrt {\left (3 x +c_1 \right ) x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.188 (sec). Leaf size: 42

DSolve[(3*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 {3 x+c_1} \\ y(x)\to \sqrt {x} \sqrt {3 x+c_1} \\ \end{align*}