29.3.25 problem 79

Internal problem ID [4687]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 3
Problem number : 79
Date solved : Sunday, March 30, 2025 at 03:36:47 AM
CAS classification : [_Abel]

\begin{align*} y^{\prime }+3 a \left (2 x +y\right ) y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 57

ode:=diff(y(x),x)+3*a*(y(x)+2*x)*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{3 a \,x^{2}+\operatorname {RootOf}\left (3^{{1}/{3}} \left (-a \right )^{{1}/{3}} \operatorname {AiryBi}\left (\textit {\_Z} \right ) c_1 x +3^{{1}/{3}} \left (-a \right )^{{1}/{3}} x \operatorname {AiryAi}\left (\textit {\_Z} \right )+\operatorname {AiryBi}\left (1, \textit {\_Z}\right ) c_1 +\operatorname {AiryAi}\left (1, \textit {\_Z}\right )\right ) 3^{{1}/{3}} \left (-a \right )^{{1}/{3}}} \]

✓ Mathematica. Time used: 0.304 (sec). Leaf size: 185

ode=D[y[x],x]+3 a(2 x + y[x])y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {\sqrt [3]{-3} \sqrt [3]{a} x \operatorname {AiryAi}\left ((-3)^{2/3} a^{2/3} x^2-\frac {(-1)^{2/3}}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )+\operatorname {AiryAiPrime}\left ((-3)^{2/3} a^{2/3} x^2-\frac {(-1)^{2/3}}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )}{\sqrt [3]{-3} \sqrt [3]{a} x \operatorname {AiryBi}\left ((-3)^{2/3} a^{2/3} x^2-\frac {(-1)^{2/3}}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )+\operatorname {AiryBiPrime}\left ((-3)^{2/3} a^{2/3} x^2-\frac {(-1)^{2/3}}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )}+c_1=0,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(3*a*(2*x + y(x))*y(x)**2 + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -3*a*(-2*x - y(x))*y(x)**2 + Derivative(y(x), x) cannot be solved by the factorable group method