Internal problem ID [10127]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 12. Equations of
form \(y f_1(x y)+x f_2( xy) y'=0\). Page 18
Problem number: Ex 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {2 y+3 y^{2} x +\left (x +2 x^{2} y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 43
dsolve((2*y(x)+3*x*y(x)^2)+(x+2*x^2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-x +\sqrt {x^{2}+4 x c_{1}}}{2 x^{2}} \\ y \relax (x ) = -\frac {x +\sqrt {x^{2}+4 x c_{1}}}{2 x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.627 (sec). Leaf size: 69
DSolve[(2*y[x]+3*x*y[x]^2)+(x+2*x^2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^{3/2}+\sqrt {x^2 (x+4 c_1)}}{2 x^{5/2}} \\ y(x)\to \frac {-x^{3/2}+\sqrt {x^2 (x+4 c_1)}}{2 x^{5/2}} \\ \end{align*}