54.2.21 problem 24

Internal problem ID [8553]
Book : Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition. 1997.
Section : CHAPTER 16. Nonlinear equations. Miscellaneous Exercises. Page 340
Problem number : 24
Date solved : Monday, January 27, 2025 at 04:14:05 PM
CAS classification : [_quadrature]

\begin{align*} x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

dsolve(x*diff(y(x),x)^2+y(x)*(1-x)*diff(y(x),x)-y(x)^2=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 26

DSolve[x*D[y[x],x]^2+y[x]*(1-x)*D[y[x],x]-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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