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 : Sunday, March 30, 2025 at 01:17:32 PM
CAS classification : [_linear]

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

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

ode:=x^2*diff(y(x),x)^2 = (x-y(x))^2; 
dsolve(ode,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*}

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

ode=x^2*D[y[x],x]^2==(x-y[x])^2; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.260 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x)**2 - (x - y(x))**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = x \left (C_{1} - \log {\left (x \right )}\right ), \ y{\left (x \right )} = \frac {C_{1}}{x} + \frac {x}{2}\right ] \]