29.35.11 problem 1043
Internal
problem
ID
[5609]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
35
Problem
number
:
1043
Date
solved
:
Tuesday, March 04, 2025 at 10:42:39 PM
CAS
classification
:
[[_homogeneous, `class C`], _dAlembert]
\begin{align*} {y^{\prime }}^{3}-a {y^{\prime }}^{2}+b y+a b x&=0 \end{align*}
✓ Maple. Time used: 0.134 (sec). Leaf size: 132
ode:=diff(y(x),x)^3-a*diff(y(x),x)^2+b*y(x)+a*b*x = 0;
dsolve(ode,y(x), singsol=all);
\[
y \left (x \right ) = \frac {-{\mathrm e}^{3 \operatorname {RootOf}\left (-10 \textit {\_Z} \,a^{2}-3 \,{\mathrm e}^{2 \textit {\_Z}}+16 a \,{\mathrm e}^{\textit {\_Z}}+2 c_{1} b -13 a^{2}-2 b x \right )}+4 \,{\mathrm e}^{2 \operatorname {RootOf}\left (-10 \textit {\_Z} \,a^{2}-3 \,{\mathrm e}^{2 \textit {\_Z}}+16 a \,{\mathrm e}^{\textit {\_Z}}+2 c_{1} b -13 a^{2}-2 b x \right )} a -5 \,{\mathrm e}^{\operatorname {RootOf}\left (-10 \textit {\_Z} \,a^{2}-3 \,{\mathrm e}^{2 \textit {\_Z}}+16 a \,{\mathrm e}^{\textit {\_Z}}+2 c_{1} b -13 a^{2}-2 b x \right )} a^{2}+2 a^{3}-b x a}{b}
\]
✓ Mathematica. Time used: 0.711 (sec). Leaf size: 398
ode=(D[y[x],x])^3 - a*(D[y[x],x])^2 +b*y[x]+a*b*x==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [\left \{x=\frac {5 a \left (\frac {\sqrt [3]{2 a^3+\sqrt {\left (2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}{3 \sqrt [3]{2}}+\frac {\sqrt [3]{2} a^2}{3 \sqrt [3]{2 a^3+\sqrt {\left (2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}+\frac {a}{3}\right )-\frac {3}{2} \left (\frac {\sqrt [3]{2 a^3+\sqrt {\left (2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}{3 \sqrt [3]{2}}+\frac {\sqrt [3]{2} a^2}{3 \sqrt [3]{2 a^3+\sqrt {\left (2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}+\frac {a}{3}\right )^2-5 a^2 \log \left (\frac {\sqrt [3]{2 a^3+\sqrt {\left (2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}{3 \sqrt [3]{2}}+\frac {\sqrt [3]{2} a^2}{3 \sqrt [3]{2 a^3+\sqrt {\left (2 a^3-27 a b x-27 b y(x)\right )^2-4 a^6}-27 a b x-27 b y(x)}}+\frac {4 a}{3}\right )}{b}+c_1\right \},y(x)\right ]
\]
✗ Sympy
from sympy import *
x = symbols("x")
a = symbols("a")
b = symbols("b")
y = Function("y")
ode = Eq(a*b*x - a*Derivative(y(x), x)**2 + b*y(x) + Derivative(y(x), x)**3,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
Timed Out