60.1.230 problem 235

Internal problem ID [10244]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 235
Date solved : Sunday, March 30, 2025 at 03:34:00 PM
CAS classification : [[_1st_order, _with_exponential_symmetries], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 30

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

\[ c_1 +\frac {1}{-{\mathrm e}^{\frac {y}{b}} b x +a \,\operatorname {Ei}_{1}\left (-\frac {y}{b}\right )} = 0 \]

✓ Mathematica. Time used: 0.084 (sec). Leaf size: 54

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

\[ \text {Solve}\left [x=e^{-\frac {y(x)}{b}} \int _1^{y(x)}-\frac {a e^{\frac {K[1]}{b}}}{b K[1]}dK[1]+c_1 e^{-\frac {y(x)}{b}},y(x)\right ] \]

✓ Sympy. Time used: 1.115 (sec). Leaf size: 20

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

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