53.1.11 problem 11

Internal problem ID [8445]
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 : 11
Date solved : Monday, January 27, 2025 at 04:01:10 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 26

dsolve(diff(y(x),x)^2-x*y(x)*(x+y(x))*diff(y(x),x)+x^3*y(x)^3=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.163 (sec). Leaf size: 38

DSolve[(D[y[x],x])^2-x*y[x]*(x+y[x])*D[y[x],x]+x^3*y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
 

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