23.1.501 problem 491
Internal
problem
ID
[5108]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Part
II.
Chapter
1.
THE
DIFFERENTIAL
EQUATION
IS
OF
FIRST
ORDER
AND
OF
FIRST
DEGREE,
page
223
Problem
number
:
491
Date
solved
:
Tuesday, September 30, 2025 at 11:37:40 AM
CAS
classification
:
[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} \left (11-11 x -4 y\right ) y^{\prime }&=62-8 x -25 y \end{align*}
✓ Maple. Time used: 0.205 (sec). Leaf size: 119
ode:=(11-11*x-4*y(x))*diff(y(x),x) = 62-8*x-25*y(x);
dsolve(ode,y(x), singsol=all);
\[
y = \frac {\frac {2}{9}+\frac {\left (1-i \sqrt {3}\right ) \left (12 \sqrt {3}\, \sqrt {-32+177147 \left (x -\frac {1}{9}\right )^{2} c_1^{2}}+\left (-8748 x +972\right ) c_1 \right )^{{2}/{3}}}{108}+\frac {2 i \sqrt {3}}{9}+2 \left (12 \sqrt {3}\, \sqrt {-32+177147 \left (x -\frac {1}{9}\right )^{2} c_1^{2}}-8748 c_1 x +972 c_1 \right )^{{1}/{3}} \left (2 x +1\right ) c_1}{\left (12 \sqrt {3}\, \sqrt {-32+177147 \left (x -\frac {1}{9}\right )^{2} c_1^{2}}+\left (-8748 x +972\right ) c_1 \right )^{{1}/{3}} c_1}
\]
✓ Mathematica. Time used: 60.12 (sec). Leaf size: 1677
ode=(11-11 x-4*y[x])*D[y[x],x]==62-8*x -25*y[x];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
Too large to display
✓ Sympy. Time used: 132.311 (sec). Leaf size: 410
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(8*x + (-11*x - 4*y(x) + 11)*Derivative(y(x), x) + 25*y(x) - 62,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\left [ y{\left (x \right )} = \frac {- \frac {2 \cdot 6^{\frac {2}{3}} i C_{1}}{3 \sqrt [3]{C_{1} \left (- 81 x + \sqrt {3} \sqrt {- 16 C_{1} + 2187 x^{2} - 486 x + 27} + 9\right )}} + 4 \sqrt {3} x - 4 i x + \frac {\sqrt [3]{2} \cdot 3^{\frac {5}{6}} \sqrt [3]{C_{1} \left (- 81 x + \sqrt {3} \sqrt {- 16 C_{1} + 2187 x^{2} - 486 x + 27} + 9\right )}}{6} + \frac {\sqrt [3]{6} i \sqrt [3]{C_{1} \left (- 81 x + \sqrt {3} \sqrt {- 16 C_{1} + 2187 x^{2} - 486 x + 27} + 9\right )}}{6} + 2 \sqrt {3} - 2 i}{\sqrt {3} - i}, \ y{\left (x \right )} = \frac {\frac {2 \cdot 6^{\frac {2}{3}} i C_{1}}{3 \sqrt [3]{C_{1} \left (- 81 x + \sqrt {3} \sqrt {- 16 C_{1} + 2187 x^{2} - 486 x + 27} + 9\right )}} + 4 \sqrt {3} x + 4 i x + \frac {\sqrt [3]{2} \cdot 3^{\frac {5}{6}} \sqrt [3]{C_{1} \left (- 81 x + \sqrt {3} \sqrt {- 16 C_{1} + 2187 x^{2} - 486 x + 27} + 9\right )}}{6} - \frac {\sqrt [3]{6} i \sqrt [3]{C_{1} \left (- 81 x + \sqrt {3} \sqrt {- 16 C_{1} + 2187 x^{2} - 486 x + 27} + 9\right )}}{6} + 2 \sqrt {3} + 2 i}{\sqrt {3} + i}, \ y{\left (x \right )} = - \frac {6^{\frac {2}{3}} C_{1}}{3 \sqrt [3]{C_{1} \left (- 81 x + \sqrt {3} \sqrt {- 16 C_{1} + 2187 x^{2} - 486 x + 27} + 9\right )}} + 4 x - \frac {\sqrt [3]{6} \sqrt [3]{C_{1} \left (- 81 x + \sqrt {3} \sqrt {- 16 C_{1} + 2187 x^{2} - 486 x + 27} + 9\right )}}{6} + 2\right ]
\]