60.1.233 problem 238

Internal problem ID [10247]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 238
Date solved : Sunday, March 30, 2025 at 03:34:11 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 91

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

\begin{align*} y &= \frac {c_1 a b x +x +\sqrt {\left (a +b \right ) \left (-1+\left (a \,x^{2}+b \,x^{2}+a^{2}\right ) c_1 \right )}}{c_1 \,a^{2}-1} \\ y &= \frac {c_1 a b x +x -\sqrt {\left (a +b \right ) \left (-1+\left (a \,x^{2}+b \,x^{2}+a^{2}\right ) c_1 \right )}}{c_1 \,a^{2}-1} \\ \end{align*}

✓ Mathematica. Time used: 2.794 (sec). Leaf size: 1598

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 84.276 (sec). Leaf size: 37

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

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