69.1.55 problem 74
Internal
problem
ID
[14137]
Book
:
DIFFERENTIAL
and
INTEGRAL
CALCULUS.
VOL
I.
by
N.
PISKUNOV.
MIR
PUBLISHERS,
Moscow
1969.
Section
:
Chapter
8.
Differential
equations.
Exercises
page
595
Problem
number
:
74
Date
solved
:
Monday, March 31, 2025 at 12:10:16 PM
CAS
classification
:
[[_homogeneous, `class G`], _exact, _rational]
\begin{align*} \left (y^{3}-x \right ) y^{\prime }&=y \end{align*}
✓ Maple. Time used: 0.006 (sec). Leaf size: 18
ode:=(y(x)^3-x)*diff(y(x),x) = y(x);
dsolve(ode,y(x), singsol=all);
\[
-\frac {c_1}{y}+x -\frac {y^{3}}{4} = 0
\]
✓ Mathematica. Time used: 35.568 (sec). Leaf size: 996
ode=(y[x]^3-x)*D[y[x],x]==y[x];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} \text {Solution too large to show}\end{align*}
✓ Sympy. Time used: 55.371 (sec). Leaf size: 648
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq((-x + y(x)**3)*Derivative(y(x), x) - y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = - \frac {\sqrt {- \frac {8 C_{1}}{3 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}} + 2 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}}}{2} - \frac {\sqrt {\frac {8 C_{1}}{3 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}} - \frac {8 x}{\sqrt {- \frac {8 C_{1}}{3 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}} + 2 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}}} - 2 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}}}{2}, \ y{\left (x \right )} = - \frac {\sqrt {- \frac {8 C_{1}}{3 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}} + 2 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}}}{2} + \frac {\sqrt {\frac {8 C_{1}}{3 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}} - \frac {8 x}{\sqrt {- \frac {8 C_{1}}{3 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}} + 2 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}}} - 2 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}}}{2}, \ y{\left (x \right )} = \frac {\sqrt {- \frac {8 C_{1}}{3 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}} + 2 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}}}{2} - \frac {\sqrt {\frac {8 C_{1}}{3 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}} + \frac {8 x}{\sqrt {- \frac {8 C_{1}}{3 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}} + 2 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}}} - 2 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}}}{2}, \ y{\left (x \right )} = \frac {\sqrt {- \frac {8 C_{1}}{3 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}} + 2 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}}}{2} + \frac {\sqrt {\frac {8 C_{1}}{3 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}} + \frac {8 x}{\sqrt {- \frac {8 C_{1}}{3 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}} + 2 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}}} - 2 \sqrt [3]{x^{2} + \sqrt {\frac {64 C_{1}^{3}}{27} + x^{4}}}}}{2}\right ]
\]