23.2.355 problem 406

Internal problem ID [5710]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 406
Date solved : Tuesday, September 30, 2025 at 02:01:39 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} a \left (\ln \left (y^{\prime }\right )-y^{\prime }\right )-x +y&=0 \end{align*}

✓ Maple. Time used: 0.054 (sec). Leaf size: 39

ode:=a*(ln(diff(y(x),x))-diff(y(x),x))-x+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.215 (sec). Leaf size: 22

ode=a*(Log[D[y[x],x]]-D[y[x],x])-x+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to a e^{\frac {x-c_1}{a}}+c_1 \end{align*}

✓ Sympy. Time used: 0.889 (sec). Leaf size: 19

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

\[ C_{1} + a W\left (- e^{\frac {x - y{\left (x \right )}}{a}}\right ) + y{\left (x \right )} = 0 \]