53.1.10 problem 10

Internal problem ID [8444]
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 : 10
Date solved : Monday, January 27, 2025 at 04:01:05 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 34

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

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

✓ Solution by Mathematica

Time used: 0.140 (sec). Leaf size: 54

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

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