29.37.22 problem 1144

Internal problem ID [5680]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1144
Date solved : Tuesday, March 04, 2025 at 11:22:27 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 0.05 (sec). Leaf size: 27

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

\begin{align*} y(x)\to a+c_1 x+\log (c_1) \\ y(x)\to a+\log \left (-\frac {1}{x}\right )-1 \\ \end{align*}

✓ Sympy. Time used: 1.174 (sec). Leaf size: 17

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

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