Internal problem ID [10619]
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: 23(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {2 x^{2}+2 x y+y^{2}+\left (2 x y+x^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 73
dsolve((2*x^2+2*x*y(x)+y(x)^2)+(x^2+2*x*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {3 c_{1}^{2} x^{2}-\sqrt {-15 x^{4} c_{1}^{4}+12 x c_{1}}}{6 x \,c_{1}^{2}} \\ y \left (x \right ) = -\frac {3 c_{1}^{2} x^{2}+\sqrt {-15 x^{4} c_{1}^{4}+12 x c_{1}}}{6 x \,c_{1}^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.789 (sec). Leaf size: 150
DSolve[(2*x^2+2*x*y[x]+y[x]^2)+(x^2+2*x*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} \left (-3 x-\frac {\sqrt {3} \sqrt {-5 x^3+4 e^{3 c_1}}}{\sqrt {x}}\right ) \\ y(x)\to \frac {1}{6} \left (-3 x+\frac {\sqrt {3} \sqrt {-5 x^3+4 e^{3 c_1}}}{\sqrt {x}}\right ) \\ y(x)\to \frac {1}{6} x \left (\frac {\sqrt {15} x^{3/2}}{\sqrt {-x^3}}-3\right ) \\ y(x)\to \frac {\sqrt {\frac {5}{3}} \sqrt {-x^3}}{2 \sqrt {x}}-\frac {x}{2} \\ \end{align*}