Internal problem ID [6031]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 94. Factoring the left member. EXERCISES
Page 309
Problem number: 18.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{3}-\left (x^{2}+x +y\right ) \left (y^{\prime }\right )^{2}+\left (x^{2}+x y+y\right ) y^{\prime }-x y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 23
dsolve(x*diff(y(x),x)^3-(x^2+x+y(x))*diff(y(x),x)^2+(x^2+x*y(x)+y(x))*diff(y(x),x)-x*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1} x \\ y \relax (x ) = c_{1}+x \\ y \relax (x ) = \frac {x^{2}}{2}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 36
DSolve[x*(y'[x])^3-(x^2+x+y[x])*(y'[x])^2+(x^2+x*y[x]+y[x])*y'[x]-x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x \\ y(x)\to x+c_1 \\ y(x)\to \frac {x^2}{2}+c_1 \\ y(x)\to 0 \\ \end{align*}