60.1.285 problem 291

Internal problem ID [10299]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 291
Date solved : Sunday, March 30, 2025 at 03:53:38 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

\begin{align*} \left (b \left (\beta y+\alpha x \right )^{2}-\beta \left (b y+a x \right )\right ) y^{\prime }+a \left (\beta y+\alpha x \right )^{2}-\alpha \left (b y+a x \right )&=0 \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 50

ode:=(b*(beta*y(x)+alpha*x)^2-beta*(a*x+b*y(x)))*diff(y(x),x)+a*(beta*y(x)+alpha*x)^2-alpha*(a*x+b*y(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-a x +{\mathrm e}^{\operatorname {RootOf}\left (c_1 a \beta x -c_1 \alpha b x -\textit {\_Z} a \beta x +\textit {\_Z} \alpha b x -c_1 \beta \,{\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} \textit {\_Z} \beta +b \right )}}{b} \]

✓ Mathematica. Time used: 0.733 (sec). Leaf size: 39

ode=(b*(\[Beta]*y[x]+alpha*x)^2-\[Beta]*(b*y[x]+a*x))*D[y[x],x]+a*(\[Beta]*y[x]+alpha*x)^2-alpha*(b*y[x]+a*x)==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {a \beta \left (\log (a x+b y(x))+\frac {1}{\alpha x+\beta y(x)}\right )}{a \beta -\alpha b}=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
Alpha = symbols("Alpha") 
BETA = symbols("BETA") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
ode = Eq(-Alpha*(a*x + b*y(x)) + a*(Alpha*x + BETA*y(x))**2 + (-BETA*(a*x + b*y(x)) + b*(Alpha*x + BETA*y(x))**2)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out