64.6.15 problem 15

Internal problem ID [13365]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 05:32:27 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.085 (sec). Leaf size: 11

dsolve([(x^2+y(x)^2)-2*x*y(x)*diff(y(x),x)=0,y(1) = 2],y(x), singsol=all)
 

\[ y = \sqrt {x \left (x +3\right )} \]

✓ Solution by Mathematica

Time used: 0.197 (sec). Leaf size: 18

DSolve[{(x^2+y[x]^2)-2*x*y[x]*D[y[x],x]==0,{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {x} \sqrt {x+3} \]