Internal problem ID [11689]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {y^{2}-2 x y y^{\prime }=-x^{2}} \] With initial conditions \begin {align*} [y \left (1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 13
dsolve([(x^2+y(x)^2)-2*x*y(x)*diff(y(x),x)=0,y(1) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {\left (x +3\right ) x} \]
✓ Solution by Mathematica
Time used: 0.175 (sec). Leaf size: 18
DSolve[{(x^2+y[x]^2)-2*x*y[x]*y'[x]==0,{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {x} \sqrt {x+3} \]