Internal problem ID [10170]
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]
Solve \begin {gather*} \boxed {x y^{2} \left (3 y+y^{\prime } x \right )+y^{\prime } x -2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (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 \relax (x ) = \frac {c_{1}-\sqrt {4 x^{5}+c_{1}^{2}}}{2 x^{3}} \\ y \relax (x ) = \frac {c_{1}+\sqrt {4 x^{5}+c_{1}^{2}}}{2 x^{3}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.062 (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*}