Internal problem ID [10615]
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: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {3 x^{2}+9 x y+5 y^{2}-\left (6 x^{2}+4 x y\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (2\right ) = -6] \end {align*}
✓ Solution by Maple
Time used: 0.329 (sec). Leaf size: 21
dsolve([(3*x^2+9*x*y(x)+5*y(x)^2)-(6*x^2+4*x*y(x))*diff(y(x),x)=0,y(2) = -6],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (3+\sqrt {-3+6 \sqrt {x}\, \sqrt {2}}\right ) x}{2} \]
✓ Solution by Mathematica
Time used: 21.827 (sec). Leaf size: 30
DSolve[{(3*x^2+9*x*y[x]+5*y[x]^2)-(6*x^2+4*x*y[x])*y'[x]==0,{y[2]==-6}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} \left (\sqrt {6 \sqrt {2} \sqrt {x}-3}+3\right ) x \\ \end{align*}