60.1.13 problem 13

Internal problem ID [10027]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 13
Date solved : Sunday, March 30, 2025 at 02:54:07 PM
CAS classification : [_Riccati]

\begin{align*} y^{\prime }+y^{2}-a x -b&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 73

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

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

✓ Mathematica. Time used: 0.175 (sec). Leaf size: 105

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

\begin{align*} y(x)\to \frac {\sqrt [3]{a} \left (\operatorname {AiryBiPrime}\left (\frac {b+a x}{a^{2/3}}\right )+c_1 \operatorname {AiryAiPrime}\left (\frac {b+a x}{a^{2/3}}\right )\right )}{\operatorname {AiryBi}\left (\frac {b+a x}{a^{2/3}}\right )+c_1 \operatorname {AiryAi}\left (\frac {b+a x}{a^{2/3}}\right )} \\ y(x)\to \frac {\sqrt [3]{a} \operatorname {AiryAiPrime}\left (\frac {b+a x}{a^{2/3}}\right )}{\operatorname {AiryAi}\left (\frac {b+a x}{a^{2/3}}\right )} \\ \end{align*}

✗ Sympy

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

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