57.1.30 problem 30
Internal
problem
ID
[9014]
Book
:
First
order
enumerated
odes
Section
:
section
1
Problem
number
:
30
Date
solved
:
Wednesday, March 05, 2025 at 07:14:43 AM
CAS
classification
:
[_Riccati]
\begin{align*} y^{\prime }&=x +y+b y^{2} \end{align*}
✓ Maple. Time used: 0.016 (sec). Leaf size: 105
ode:=diff(y(x),x) = x+y(x)+b*y(x)^2;
dsolve(ode,y(x), singsol=all);
\[
y = \frac {2 b^{{1}/{3}} \operatorname {AiryAi}\left (1, -\frac {4 b x -1}{4 b^{{2}/{3}}}\right ) c_{1} +2 \operatorname {AiryBi}\left (1, -\frac {4 b x -1}{4 b^{{2}/{3}}}\right ) b^{{1}/{3}}-\operatorname {AiryAi}\left (-\frac {4 b x -1}{4 b^{{2}/{3}}}\right ) c_{1} -\operatorname {AiryBi}\left (-\frac {4 b x -1}{4 b^{{2}/{3}}}\right )}{2 b \left (\operatorname {AiryAi}\left (-\frac {4 b x -1}{4 b^{{2}/{3}}}\right ) c_{1} +\operatorname {AiryBi}\left (-\frac {4 b x -1}{4 b^{{2}/{3}}}\right )\right )}
\]
✓ Mathematica. Time used: 0.205 (sec). Leaf size: 211
ode=D[y[x],x]==x+y[x]+b*y[x]^2;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to -\frac {-(-b)^{2/3} \operatorname {AiryBi}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )+2 b \operatorname {AiryBiPrime}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )+c_1 \left (2 b \operatorname {AiryAiPrime}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )-(-b)^{2/3} \operatorname {AiryAi}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )\right )}{2 (-b)^{5/3} \left (\operatorname {AiryBi}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )+c_1 \operatorname {AiryAi}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )\right )} \\
y(x)\to -\frac {\frac {2 \sqrt [3]{-b} \operatorname {AiryAiPrime}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )}{\operatorname {AiryAi}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )}+1}{2 b} \\
\end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
b = symbols("b")
y = Function("y")
ode = Eq(-b*y(x)**2 - x - y(x) + Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
TypeError : bad operand type for unary -: list