54.2.18 problem 21

Internal problem ID [8550]
Book : Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition. 1997.
Section : CHAPTER 16. Nonlinear equations. Miscellaneous Exercises. Page 340
Problem number : 21
Date solved : Monday, January 27, 2025 at 04:13:59 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

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

\begin{align*} y &= \left (-\ln \left (x \right )+c_{1} \right ) x \\ y &= \frac {x}{2}+\frac {c_{1}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.079 (sec). Leaf size: 30

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

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