66.1.16 problem Problem 16
Internal
problem
ID
[13792]
Book
:
Differential
equations
and
the
calculus
of
variations
by
L.
ElSGOLTS.
MIR
PUBLISHERS,
MOSCOW,
Third
printing
1977.
Section
:
Chapter
1,
First-Order
Differential
Equations.
Problems
page
88
Problem
number
:
Problem
16
Date
solved
:
Monday, March 31, 2025 at 08:12:18 AM
CAS
classification
:
[_quadrature]
\begin{align*} x&={y^{\prime }}^{3}-y^{\prime }+2 \end{align*}
✓ Maple. Time used: 0.033 (sec). Leaf size: 207
ode:=x = diff(y(x),x)^3-diff(y(x),x)+2;
dsolve(ode,y(x), singsol=all);
\begin{align*}
y &= -\frac {\int \frac {i \sqrt {3}\, \left (-216+108 x +12 \sqrt {81 x^{2}-324 x +312}\right )^{{2}/{3}}-12 i \sqrt {3}+\left (-216+108 x +12 \sqrt {81 x^{2}-324 x +312}\right )^{{2}/{3}}+12}{\left (-216+108 x +12 \sqrt {81 x^{2}-324 x +312}\right )^{{1}/{3}}}d x}{12}+c_1 \\
y &= \frac {\int \frac {\left (i \sqrt {3}-1\right ) \left (-216+108 x +12 \sqrt {81 x^{2}-324 x +312}\right )^{{2}/{3}}-12 i \sqrt {3}-12}{\left (-216+108 x +12 \sqrt {81 x^{2}-324 x +312}\right )^{{1}/{3}}}d x}{12}+c_1 \\
y &= \frac {\int \frac {\left (-216+108 x +12 \sqrt {81 x^{2}-324 x +312}\right )^{{2}/{3}}+12}{\left (-216+108 x +12 \sqrt {81 x^{2}-324 x +312}\right )^{{1}/{3}}}d x}{6}+c_1 \\
\end{align*}
✗ Mathematica
ode=x==D[y[x],x]^3-D[y[x],x]+2;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
Timed out
✓ Sympy. Time used: 13.523 (sec). Leaf size: 342
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(x - Derivative(y(x), x)**3 + Derivative(y(x), x) - 2,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = C_{1} + \frac {i \left (- 4 \sqrt [3]{2} \cdot 3^{\frac {2}{3}} \int \frac {1}{\sqrt [3]{- 9 x + \sqrt {3} \sqrt {27 x^{2} - 108 x + 104} + 18}}\, dx + \sqrt [3]{12} \int \sqrt [3]{- 9 x + \sqrt {3} \sqrt {27 x^{2} - 108 x + 104} + 18}\, dx - 2^{\frac {2}{3}} \cdot 3^{\frac {5}{6}} i \int \sqrt [3]{- 9 x + \sqrt {3} \sqrt {27 x^{2} - 108 x + 104} + 18}\, dx\right )}{6 \left (\sqrt {3} - i\right )}, \ y{\left (x \right )} = C_{1} - \frac {i \left (- 4 \sqrt [3]{2} \cdot 3^{\frac {2}{3}} \int \frac {1}{\sqrt [3]{- 9 x + \sqrt {3} \sqrt {27 x^{2} - 108 x + 104} + 18}}\, dx + \sqrt [3]{12} \int \sqrt [3]{- 9 x + \sqrt {3} \sqrt {27 x^{2} - 108 x + 104} + 18}\, dx + 2^{\frac {2}{3}} \cdot 3^{\frac {5}{6}} i \int \sqrt [3]{- 9 x + \sqrt {3} \sqrt {27 x^{2} - 108 x + 104} + 18}\, dx\right )}{6 \left (\sqrt {3} + i\right )}, \ y{\left (x \right )} = C_{1} - \frac {\sqrt [3]{18} \int \frac {1}{\sqrt [3]{- 9 x + \sqrt {3} \sqrt {27 x^{2} - 108 x + 104} + 18}}\, dx}{3} - \frac {\sqrt [3]{12} \int \sqrt [3]{- 9 x + \sqrt {3} \sqrt {27 x^{2} - 108 x + 104} + 18}\, dx}{6}\right ]
\]