29.3.27 problem 81
Internal
problem
ID
[4689]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
3
Problem
number
:
81
Date
solved
:
Tuesday, March 04, 2025 at 07:03:01 PM
CAS
classification
:
[_quadrature]
\begin{align*} y^{\prime }&=\operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3} \end{align*}
✓ Maple. Time used: 0.003 (sec). Leaf size: 30
ode:=diff(y(x),x) = a0+a1*y(x)+a2*y(x)^2+a3*y(x)^3;
dsolve(ode,y(x), singsol=all);
\[
x -\int _{}^{y \left (x \right )}\frac {1}{\textit {\_a}^{3} \operatorname {a3} +\textit {\_a}^{2} \operatorname {a2} +\textit {\_a} \operatorname {a1} +\operatorname {a0}}d \textit {\_a} +c_{1} = 0
\]
✓ Mathematica. Time used: 0.115 (sec). Leaf size: 54
ode=D[y[x],x]==a0+a1 y[x]+a2 y[x]^2+ a3 y[x]^3;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3 \text {a3}+\text {$\#$1}^2 \text {a2}+\text {$\#$1} \text {a1}+\text {a0}\&,\frac {\log (y(x)-\text {$\#$1})}{3 \text {$\#$1}^2 \text {a3}+2 \text {$\#$1} \text {a2}+\text {a1}}\&\right ]=x+c_1,y(x)\right ]
\]
✓ Sympy. Time used: 56.596 (sec). Leaf size: 274
from sympy import *
x = symbols("x")
a0 = symbols("a0")
a1 = symbols("a1")
a2 = symbols("a2")
a3 = symbols("a3")
y = Function("y")
ode = Eq(-a0 - a1*y(x) - a2*y(x)**2 - a3*y(x)**3 + Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
- \operatorname {RootSum} {\left (t^{3} \left (27 a_{0}^{2} a_{3}^{2} - 18 a_{0} a_{1} a_{2} a_{3} + 4 a_{0} a_{2}^{3} + 4 a_{1}^{3} a_{3} - a_{1}^{2} a_{2}^{2}\right ) + t \left (- 3 a_{1} a_{3} + a_{2}^{2}\right ) - a_{3}, \left ( t \mapsto t \log {\left (y{\left (x \right )} + \frac {- 162 t^{2} a_{0}^{2} a_{1} a_{3}^{3} + 54 t^{2} a_{0}^{2} a_{2}^{2} a_{3}^{2} + 108 t^{2} a_{0} a_{1}^{2} a_{2} a_{3}^{2} - 60 t^{2} a_{0} a_{1} a_{2}^{3} a_{3} + 8 t^{2} a_{0} a_{2}^{5} - 24 t^{2} a_{1}^{4} a_{3}^{2} + 14 t^{2} a_{1}^{3} a_{2}^{2} a_{3} - 2 t^{2} a_{1}^{2} a_{2}^{4} + 81 t a_{0}^{2} a_{3}^{3} - 54 t a_{0} a_{1} a_{2} a_{3}^{2} + 12 t a_{0} a_{2}^{3} a_{3} + 12 t a_{1}^{3} a_{3}^{2} - 3 t a_{1}^{2} a_{2}^{2} a_{3} + 9 a_{0} a_{2} a_{3}^{2} + 12 a_{1}^{2} a_{3}^{2} - 11 a_{1} a_{2}^{2} a_{3} + 2 a_{2}^{4}}{a_{3} \left (27 a_{0} a_{3}^{2} - 9 a_{1} a_{2} a_{3} + 2 a_{2}^{3}\right )} \right )} \right )\right )} = C_{1} - x
\]