Internal problem ID [11194]
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 19.
Summary. Page 29
Problem number: Ex 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {x y^{2} \left (3 y+y^{\prime } x \right )-2 y+y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 45
dsolve((x*y(x)^2)*(3*y(x)+x*diff(y(x),x))-(2*y(x)-x*diff(y(x),x))=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {c_{1} +\sqrt {4 x^{5}+c_{1}^{2}}}{2 x^{3}} y \left (x \right ) = -\frac {-c_{1} +\sqrt {4 x^{5}+c_{1}^{2}}}{2 x^{3}} \end{align*}
✓ Solution by Mathematica
Time used: 1.836 (sec). Leaf size: 75
DSolve[(x*y[x]^2)*(3*y[x]+x*y'[x])-(2*y[x]-x*y'[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {4 x^5+e^{5 c_1}}+e^{\frac {5 c_1}{2}}}{2 x^3} y(x)\to \frac {\sqrt {4 x^5+e^{5 c_1}}-e^{\frac {5 c_1}{2}}}{2 x^3} \end{align*}