Internal problem ID [11631]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {3 y^{2}-2 x y y^{\prime }=-x^{2}} \] With initial conditions \begin {align*} [y \left (2\right ) = 6] \end {align*}
✓ Solution by Maple
Time used: 0.062 (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)
\[ y \left (x \right ) = \sqrt {5 x -1}\, x \]
✓ Solution by Mathematica
Time used: 0.455 (sec). Leaf size: 16
DSolve[{(x^2+3*y[x]^2)-2*x*y[x]*y'[x]==0,{y[2]==6}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \sqrt {5 x-1} \]