Internal problem ID [6882]
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.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_linear]
\[ \boxed {x^{2} {y^{\prime }}^{2}-\left (x -y\right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(x^2*diff(y(x),x)^2=(x-y(x))^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \left (-\ln \left (x \right )+c_{1} \right ) x y \left (x \right ) = \frac {x}{2}+\frac {c_{1}}{x} \end{align*}
✓ Solution by Mathematica
Time used: 0.073 (sec). Leaf size: 30
DSolve[x^2*y'[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*}