90.12.1 problem 1

Internal problem ID [25203]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 3. Second Order Constant Coefficient Linear Differential Equations. Exercises at page 213
Problem number : 1
Date solved : Friday, October 03, 2025 at 08:08:38 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }-y y^{\prime }&=6 \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 60

ode:=diff(diff(y(t),t),t)-y(t)*diff(y(t),t) = 6; 
dsolve(ode,y(t), singsol=all);
 

\[ 2 \,3^{{1}/{3}} \int _{}^{y}\frac {1}{3^{{1}/{3}} \textit {\_a}^{2}-12 \operatorname {RootOf}\left (\operatorname {AiryBi}\left (\textit {\_Z} \right ) 3^{{2}/{3}} c_1 \textit {\_a} +3^{{2}/{3}} \textit {\_a} \operatorname {AiryAi}\left (\textit {\_Z} \right )-6 \operatorname {AiryBi}\left (1, \textit {\_Z}\right ) c_1 -6 \operatorname {AiryAi}\left (1, \textit {\_Z}\right )\right )}d \textit {\_a} -t -c_2 = 0 \]

✓ Mathematica. Time used: 98.638 (sec). Leaf size: 114

ode=D[y[t],{t,2}]-y[t]*D[y[t],t]==6; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {2 \sqrt [3]{-3} \left (c_2 \operatorname {AiryAiPrime}\left (\frac {\sqrt [3]{-1} (6 t-c_1)}{2\ 3^{2/3}}\right )+\operatorname {AiryBiPrime}\left (\frac {\sqrt [3]{-1} (6 t-c_1)}{2\ 3^{2/3}}\right )\right )}{c_2 \operatorname {AiryAi}\left (\frac {\sqrt [3]{-1} (6 t-c_1)}{2\ 3^{2/3}}\right )+\operatorname {AiryBi}\left (\frac {\sqrt [3]{-1} (6 t-c_1)}{2\ 3^{2/3}}\right )} \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t)*Derivative(y(t), t) + Derivative(y(t), (t, 2)) - 6,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : The given ODE -(Derivative(y(t), (t, 2)) - 6)/y(t) + Derivative(y(t), t) canno