2.18 problem 21

Internal problem ID [6129]

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]

Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}-\left (x -y\right )^{2}=0} \end {gather*}

Solution by Maple

Time used: 0.002 (sec). Leaf size: 24

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

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

Solution by Mathematica

Time used: 0.071 (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*}