Internal problem ID [6113]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 16. Nonlinear equations. Miscellaneous Exercises. Page 340
Problem number: 2.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {6 x \left (y^{\prime }\right )^{2}-\left (3 x +2 y\right ) y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(6*x*diff(y(x),x)^2-(3*x+2*y(x))*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1} x^{\frac {1}{3}} \\ y \relax (x ) = \frac {x}{2}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 30
DSolve[6*x*(y'[x])^2-(3*x+2*y[x])*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \sqrt [3]{x} \\ y(x)\to \frac {x}{2}+c_1 \\ y(x)\to 0 \\ \end{align*}