23.1.631 problem 625
Internal
problem
ID
[5238]
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
:
625
Date
solved
:
Tuesday, September 30, 2025 at 11:58:15 AM
CAS
classification
:
[[_homogeneous, `class A`], _rational, _dAlembert]
\begin{align*} \left (3 x +y\right )^{2} y^{\prime }&=4 \left (3 x +2 y\right ) y \end{align*}
✓ Maple. Time used: 0.010 (sec). Leaf size: 44
ode:=(3*x+y(x))^2*diff(y(x),x) = 4*(3*x+2*y(x))*y(x);
dsolve(ode,y(x), singsol=all);
\[
-\ln \left (\frac {y+x}{x}\right )-3 \ln \left (\frac {y-3 x}{x}\right )+3 \ln \left (\frac {y}{x}\right )-\ln \left (x \right )-c_1 = 0
\]
✓ Mathematica. Time used: 60.164 (sec). Leaf size: 747
ode=(3*x+y[x])^2 *D[y[x],x]==4*(3*x+2*y[x])*y[x];
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to \frac {1}{4} \left (-\sqrt {12 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}+16 x^2-16 e^{c_1} x+e^{2 c_1}}-\sqrt {2} \sqrt {-6 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}-48 x^2+\frac {\left (-8 x+e^{c_1}\right ){}^3-72 x^2 \left (-8 x+e^{c_1}\right )}{\sqrt {12 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}+16 x^2-16 e^{c_1} x+e^{2 c_1}}}+\left (-8 x+e^{c_1}\right ){}^2}+8 x-e^{c_1}\right )\\ y(x)&\to \frac {1}{4} \left (-\sqrt {12 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}+16 x^2-16 e^{c_1} x+e^{2 c_1}}+\sqrt {2} \sqrt {-6 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}-48 x^2+\frac {\left (-8 x+e^{c_1}\right ){}^3-72 x^2 \left (-8 x+e^{c_1}\right )}{\sqrt {12 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}+16 x^2-16 e^{c_1} x+e^{2 c_1}}}+\left (-8 x+e^{c_1}\right ){}^2}+8 x-e^{c_1}\right )\\ y(x)&\to \frac {1}{4} \left (\sqrt {12 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}+16 x^2-16 e^{c_1} x+e^{2 c_1}}-\sqrt {2} \sqrt {-6 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}-48 x^2+\frac {72 x^2 \left (-8 x+e^{c_1}\right )-\left (-8 x+e^{c_1}\right ){}^3}{\sqrt {12 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}+16 x^2-16 e^{c_1} x+e^{2 c_1}}}+\left (-8 x+e^{c_1}\right ){}^2}+8 x-e^{c_1}\right )\\ y(x)&\to \frac {1}{4} \left (\sqrt {12 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}+16 x^2-16 e^{c_1} x+e^{2 c_1}}+\sqrt {2} \sqrt {-6 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}-48 x^2+\frac {72 x^2 \left (-8 x+e^{c_1}\right )-\left (-8 x+e^{c_1}\right ){}^3}{\sqrt {12 \sqrt [3]{-e^{c_1} x^4 \left (-16 x+e^{c_1}\right )}+16 x^2-16 e^{c_1} x+e^{2 c_1}}}+\left (-8 x+e^{c_1}\right ){}^2}+8 x-e^{c_1}\right ) \end{align*}
✓ Sympy. Time used: 52.112 (sec). Leaf size: 1163
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq((3*x + y(x))**2*Derivative(y(x), x) - (12*x + 8*y(x))*y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\text {Solution too large to show}
\]