60.1.286 problem 292

Internal problem ID [10300]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 292
Date solved : Sunday, March 30, 2025 at 03:53:42 PM
CAS classification : [[_homogeneous, `class C`], _rational]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 115

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

\[ y = \frac {\left (\left (b x +c \right ) \alpha -a \left (\beta x +\gamma \right )\right ) \operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {\left (\textit {\_a} a -b \right )^{2}}{\textit {\_a}^{3} a^{2}-2 \textit {\_a}^{2} a b -\textit {\_a}^{2} \alpha ^{2}+2 \textit {\_a} \alpha \beta +\textit {\_a} \,b^{2}-\beta ^{2}}d \textit {\_a} +\ln \left (a \beta x -\alpha b x +a \gamma -\alpha c \right )+c_1 \right )+b \gamma -\beta c}{a \beta -\alpha b} \]

✓ Mathematica. Time used: 3.173 (sec). Leaf size: 2296

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

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✗ Sympy

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

Timed Out