53.1.2 problem 2

Internal problem ID [8436]
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
Date solved : Monday, January 27, 2025 at 04:00:35 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (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 &= c_{1} x^{3} \\ y &= c_{1} +2 x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 26

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