Internal problem ID [6024]
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: 11.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-x y \left (x +y\right ) y^{\prime }+x^{3} y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x)^2-x*y(x)*(x+y(x))*diff(y(x),x)+x^3*y(x)^3=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {2}{-x^{2}+2 c_{1}} \\ y \relax (x ) = c_{1} {\mathrm e}^{\frac {x^{3}}{3}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.218 (sec). Leaf size: 38
DSolve[(y'[x])^2-x*y[x]*(x+y[x])*y'[x]+x^3*y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{\frac {x^3}{3}} \\ y(x)\to -\frac {2}{x^2+2 c_1} \\ y(x)\to 0 \\ \end{align*}