Internal problem ID [6014]
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: 2.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x {y^{\prime }}^{2}-\left (3 y+2 x \right ) y^{\prime }+6 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x*diff(y(x),x)^2-(2*x+3*y(x))*diff(y(x),x)+6*y(x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = c_{1} x^{3} \\ y \left (x \right ) = 2 x +c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 26
DSolve[x*(y'[x])^2-(2*x+3*y[x])*y'[x]+6*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x^3 \\ y(x)\to 2 x+c_1 \\ y(x)\to 0 \\ \end{align*}