64.4.18 problem 18

Internal problem ID [13307]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 05:17:29 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (2\right )&=6 \end{align*}

✓ Solution by Maple

Time used: 0.102 (sec). Leaf size: 13

dsolve([(x^2+3*y(x)^2)-2*x*y(x)*diff(y(x),x)=0,y(2) = 6],y(x), singsol=all)
 

\[ y = \sqrt {5 x -1}\, x \]

✓ Solution by Mathematica

Time used: 0.345 (sec). Leaf size: 16

DSolve[{(x^2+3*y[x]^2)-2*x*y[x]*D[y[x],x]==0,{y[2]==6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \sqrt {5 x-1} \]