54.2.2 problem 2

Internal problem ID [8534]
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
Date solved : Monday, January 27, 2025 at 04:09:52 PM
CAS classification : [_quadrature]

\begin{align*} 6 x {y^{\prime }}^{2}-\left (3 x +2 y\right ) y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (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 &= c_{1} x^{{1}/{3}} \\ y &= \frac {x}{2}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 30

DSolve[6*x*(D[y[x],x])^2-(3*x+2*y[x])*D[y[x],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*}