29.34.20 problem 1022
Internal
problem
ID
[5591]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
34
Problem
number
:
1022
Date
solved
:
Tuesday, March 04, 2025 at 10:31:50 PM
CAS
classification
:
[_quadrature]
\begin{align*} {y^{\prime }}^{3}+y^{\prime }+a -b x&=0 \end{align*}
✓ Maple. Time used: 0.031 (sec). Leaf size: 298
ode:=diff(y(x),x)^3+diff(y(x),x)+a-b*x = 0;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y \left (x \right ) &= \frac {\left (\int \frac {\left (i \sqrt {3}-1\right ) \left (108 b x -108 a +12 \sqrt {81 x^{2} b^{2}-162 b x a +81 a^{2}+12}\right )^{{2}/{3}}+12 i \sqrt {3}+12}{\left (108 b x -108 a +12 \sqrt {81 x^{2} b^{2}-162 b x a +81 a^{2}+12}\right )^{{1}/{3}}}d x \right )}{12}+c_{1} \\
y \left (x \right ) &= -\frac {\left (\int \frac {i \sqrt {3}\, \left (108 b x -108 a +12 \sqrt {81 x^{2} b^{2}-162 b x a +81 a^{2}+12}\right )^{{2}/{3}}+12 i \sqrt {3}+\left (108 b x -108 a +12 \sqrt {81 x^{2} b^{2}-162 b x a +81 a^{2}+12}\right )^{{2}/{3}}-12}{\left (108 b x -108 a +12 \sqrt {81 x^{2} b^{2}-162 b x a +81 a^{2}+12}\right )^{{1}/{3}}}d x \right )}{12}+c_{1} \\
y \left (x \right ) &= \frac {\left (\int \frac {\left (108 b x -108 a +12 \sqrt {81 x^{2} b^{2}-162 b x a +81 a^{2}+12}\right )^{{2}/{3}}-12}{\left (108 b x -108 a +12 \sqrt {81 x^{2} b^{2}-162 b x a +81 a^{2}+12}\right )^{{1}/{3}}}d x \right )}{6}+c_{1} \\
\end{align*}
✓ Mathematica. Time used: 2.555 (sec). Leaf size: 1086
ode=(D[y[x],x])^3 +D[y[x],x]+a-b x==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} \text {Solution too large to show}\end{align*}
✓ Sympy. Time used: 15.800 (sec). Leaf size: 464
from sympy import *
x = symbols("x")
a = symbols("a")
b = symbols("b")
y = Function("y")
ode = Eq(a - b*x + Derivative(y(x), x)**3 + Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = C_{1} + \frac {i \left (4 \sqrt [3]{2} \cdot 3^{\frac {2}{3}} \int \frac {1}{\sqrt [3]{9 a - 9 b x + \sqrt {3} \sqrt {27 a^{2} - 54 a b x + 27 b^{2} x^{2} + 4}}}\, dx + \sqrt [3]{12} \int \sqrt [3]{9 a - 9 b x + \sqrt {3} \sqrt {27 a^{2} - 54 a b x + 27 b^{2} x^{2} + 4}}\, dx - 2^{\frac {2}{3}} \cdot 3^{\frac {5}{6}} i \int \sqrt [3]{9 a - 9 b x + \sqrt {3} \sqrt {27 a^{2} - 54 a b x + 27 b^{2} x^{2} + 4}}\, dx\right )}{6 \left (\sqrt {3} - i\right )}, \ y{\left (x \right )} = C_{1} - \frac {i \left (4 \sqrt [3]{2} \cdot 3^{\frac {2}{3}} \int \frac {1}{\sqrt [3]{9 a - 9 b x + \sqrt {3} \sqrt {27 a^{2} - 54 a b x + 27 b^{2} x^{2} + 4}}}\, dx + \sqrt [3]{12} \int \sqrt [3]{9 a - 9 b x + \sqrt {3} \sqrt {27 a^{2} - 54 a b x + 27 b^{2} x^{2} + 4}}\, dx + 2^{\frac {2}{3}} \cdot 3^{\frac {5}{6}} i \int \sqrt [3]{9 a - 9 b x + \sqrt {3} \sqrt {27 a^{2} - 54 a b x + 27 b^{2} x^{2} + 4}}\, dx\right )}{6 \left (\sqrt {3} + i\right )}, \ y{\left (x \right )} = C_{1} + \frac {\sqrt [3]{18} \int \frac {1}{\sqrt [3]{9 a - 9 b x + \sqrt {3} \sqrt {27 a^{2} - 54 a b x + 27 b^{2} x^{2} + 4}}}\, dx}{3} - \frac {\sqrt [3]{12} \int \sqrt [3]{9 a - 9 b x + \sqrt {3} \sqrt {27 a^{2} - 54 a b x + 27 b^{2} x^{2} + 4}}\, dx}{6}\right ]
\]