53.1.3 problem 3

Internal problem ID [8437]
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 : 3
Date solved : Monday, January 27, 2025 at 04:00:38 PM
CAS classification : [_separable]

\begin{align*} x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }+6 y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(x^2*diff(y(x),x)^2-5*x*y(x)*diff(y(x),x)+6*y(x)^2=0,y(x), singsol=all)
 

\begin{align*} y &= c_{1} x^{3} \\ y &= c_{1} x^{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 26

DSolve[x^2*(D[y[x],x])^2-5*x*y[x]*D[y[x],x]+6*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 x^2 \\ y(x)\to c_1 x^3 \\ y(x)\to 0 \\ \end{align*}