29.2.28 problem 53
Internal
problem
ID
[4661]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
2
Problem
number
:
53
Date
solved
:
Monday, January 27, 2025 at 09:30:38 AM
CAS
classification
:
[_Riccati]
\begin{align*} y^{\prime }&=3 a +3 b x +3 b y^{2} \end{align*}
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 80
dsolve(diff(y(x),x) = 3*a+3*b*x+3*b*y(x)^2,y(x), singsol=all)
\[
y \left (x \right ) = \frac {\left (\operatorname {AiryAi}\left (1, -\frac {3^{{2}/{3}} \left (b x +a \right )}{b^{{1}/{3}}}\right ) c_{1} +\operatorname {AiryBi}\left (1, -\frac {3^{{2}/{3}} \left (b x +a \right )}{b^{{1}/{3}}}\right )\right ) 3^{{2}/{3}}}{b^{{1}/{3}} \left (3 c_{1} \operatorname {AiryAi}\left (-\frac {3^{{2}/{3}} \left (b x +a \right )}{b^{{1}/{3}}}\right )+3 \operatorname {AiryBi}\left (-\frac {3^{{2}/{3}} \left (b x +a \right )}{b^{{1}/{3}}}\right )\right )}
\]
✓ Solution by Mathematica
Time used: 0.216 (sec). Leaf size: 191
DSolve[D[y[x],x]==3*(a+b*x+ b*y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*}
y(x)\to \frac {b \left (\operatorname {AiryBiPrime}\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )+c_1 \operatorname {AiryAiPrime}\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )\right )}{\sqrt [3]{3} \left (-b^2\right )^{2/3} \left (\operatorname {AiryBi}\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )+c_1 \operatorname {AiryAi}\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )\right )} \\
y(x)\to \frac {b \operatorname {AiryAiPrime}\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )}{\sqrt [3]{3} \left (-b^2\right )^{2/3} \operatorname {AiryAi}\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )} \\
\end{align*}