83.8.3 problem 3

Internal problem ID [19058]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 3
Date solved : Monday, March 31, 2025 at 06:42:16 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.020 (sec). Leaf size: 36

ode:=(x-y(x))^2*diff(y(x),x) = a^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (a \ln \left ({\mathrm e}^{\textit {\_Z}}+2 a \right )-\textit {\_Z} a -2 \,{\mathrm e}^{\textit {\_Z}}+2 c_1 -2 a -2 x \right )}+a +x \]

✓ Mathematica. Time used: 0.161 (sec). Leaf size: 49

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

\[ \text {Solve}\left [-\left (a^2 \left (\frac {\log (a-y(x)+x)}{2 a}-\frac {\log (-a-y(x)+x)}{2 a}\right )\right )-y(x)=c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.604 (sec). Leaf size: 26

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

\[ C_{1} - \frac {a \left (\log {\left (- a + x - y{\left (x \right )} \right )} - \log {\left (a + x - y{\left (x \right )} \right )}\right )}{2} + y{\left (x \right )} = 0 \]