83.20.3 problem 3

Internal problem ID [19170]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (C) at page 56
Problem number : 3
Date solved : Monday, March 31, 2025 at 06:51:01 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.105 (sec). Leaf size: 30

ode:=x = y(x)+a*ln(diff(y(x),x)); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= x \\ y &= x -a \ln \left (-\frac {1}{{\mathrm e}^{\frac {c_1 -x}{a}}-1}\right ) \\ \end{align*}

✓ Mathematica. Time used: 3.666 (sec). Leaf size: 22

ode=x==y[x]+a*Log[D[y[x],x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to a \log \left (e^{\frac {x}{a}}+\frac {c_1}{a}\right ) \]

✓ Sympy. Time used: 0.372 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = a \log {\left (\frac {C_{1}}{a} + e^{\frac {x}{a}} \right )} \]