32.2.9 problem 9
Internal
problem
ID
[7726]
Book
:
Engineering
Mathematics.
By
K.
A.
Stroud.
5th
edition.
Industrial
press
Inc.
NY.
2001
Section
:
Program
24.
First
order
differential
equations.
Further
problems
24.
page
1068
Problem
number
:
9
Date
solved
:
Tuesday, September 30, 2025 at 05:02:35 PM
CAS
classification
:
[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\begin{align*} y-3 x +\left (4 y+3 x \right ) y^{\prime }&=0 \end{align*}
✓ Maple. Time used: 0.031 (sec). Leaf size: 47
ode:=y(x)-3*x+(4*y(x)+3*x)*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = \frac {\operatorname {RootOf}\left (\textit {\_Z}^{8} x^{2} c_1^{2}+4 \textit {\_Z}^{5} x^{2} c_1^{2}-\left (\frac {1}{x c_1}\right )^{{2}/{3}}\right )^{3} x}{2}+\frac {x}{2}
\]
✓ Mathematica. Time used: 6.685 (sec). Leaf size: 673
ode=y[x]-3*x+(4*y[x]+3*x)*D[y[x],x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to \text {Root}\left [256 \text {$\#$1}^8+512 \text {$\#$1}^7 x-512 \text {$\#$1}^6 x^2-896 \text {$\#$1}^5 x^3+800 \text {$\#$1}^4 x^4+352 \text {$\#$1}^3 x^5-576 \text {$\#$1}^2 x^6+216 \text {$\#$1} x^7-27 x^8+e^{8 c_1}\&,1\right ]\\ y(x)&\to \text {Root}\left [256 \text {$\#$1}^8+512 \text {$\#$1}^7 x-512 \text {$\#$1}^6 x^2-896 \text {$\#$1}^5 x^3+800 \text {$\#$1}^4 x^4+352 \text {$\#$1}^3 x^5-576 \text {$\#$1}^2 x^6+216 \text {$\#$1} x^7-27 x^8+e^{8 c_1}\&,2\right ]\\ y(x)&\to \text {Root}\left [256 \text {$\#$1}^8+512 \text {$\#$1}^7 x-512 \text {$\#$1}^6 x^2-896 \text {$\#$1}^5 x^3+800 \text {$\#$1}^4 x^4+352 \text {$\#$1}^3 x^5-576 \text {$\#$1}^2 x^6+216 \text {$\#$1} x^7-27 x^8+e^{8 c_1}\&,3\right ]\\ y(x)&\to \text {Root}\left [256 \text {$\#$1}^8+512 \text {$\#$1}^7 x-512 \text {$\#$1}^6 x^2-896 \text {$\#$1}^5 x^3+800 \text {$\#$1}^4 x^4+352 \text {$\#$1}^3 x^5-576 \text {$\#$1}^2 x^6+216 \text {$\#$1} x^7-27 x^8+e^{8 c_1}\&,4\right ]\\ y(x)&\to \text {Root}\left [256 \text {$\#$1}^8+512 \text {$\#$1}^7 x-512 \text {$\#$1}^6 x^2-896 \text {$\#$1}^5 x^3+800 \text {$\#$1}^4 x^4+352 \text {$\#$1}^3 x^5-576 \text {$\#$1}^2 x^6+216 \text {$\#$1} x^7-27 x^8+e^{8 c_1}\&,5\right ]\\ y(x)&\to \text {Root}\left [256 \text {$\#$1}^8+512 \text {$\#$1}^7 x-512 \text {$\#$1}^6 x^2-896 \text {$\#$1}^5 x^3+800 \text {$\#$1}^4 x^4+352 \text {$\#$1}^3 x^5-576 \text {$\#$1}^2 x^6+216 \text {$\#$1} x^7-27 x^8+e^{8 c_1}\&,6\right ]\\ y(x)&\to \text {Root}\left [256 \text {$\#$1}^8+512 \text {$\#$1}^7 x-512 \text {$\#$1}^6 x^2-896 \text {$\#$1}^5 x^3+800 \text {$\#$1}^4 x^4+352 \text {$\#$1}^3 x^5-576 \text {$\#$1}^2 x^6+216 \text {$\#$1} x^7-27 x^8+e^{8 c_1}\&,7\right ]\\ y(x)&\to \text {Root}\left [256 \text {$\#$1}^8+512 \text {$\#$1}^7 x-512 \text {$\#$1}^6 x^2-896 \text {$\#$1}^5 x^3+800 \text {$\#$1}^4 x^4+352 \text {$\#$1}^3 x^5-576 \text {$\#$1}^2 x^6+216 \text {$\#$1} x^7-27 x^8+e^{8 c_1}\&,8\right ] \end{align*}
✓ Sympy. Time used: 0.493 (sec). Leaf size: 29
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-3*x + (3*x + 4*y(x))*Derivative(y(x), x) + y(x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
\log {\left (y{\left (x \right )} \right )} = C_{1} - \log {\left (\left (\frac {x}{y{\left (x \right )}} - 2\right )^{\frac {5}{8}} \left (\frac {x}{y{\left (x \right )}} + \frac {2}{3}\right )^{\frac {3}{8}} \right )}
\]