53.1.18 problem 18

Internal problem ID [8452]
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 : 18
Date solved : Monday, January 27, 2025 at 04:02:00 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 36

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

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