38.2.9 problem 9
Internal
problem
ID
[6438]
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
:
Wednesday, March 05, 2025 at 12:43:34 AM
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: 0.164 (sec). Leaf size: 278
ode:=y(x)-3*x+(4*y(x)+3*x)*diff(y(x),x) = 0;
dsolve(ode,y(x), singsol=all);
\[
y = \frac {-3 x^{8} c_1 \operatorname {RootOf}\left (x^{8} c_1 \,\textit {\_Z}^{64}+12 x^{8} c_1 \,\textit {\_Z}^{56}+48 x^{8} c_1 \,\textit {\_Z}^{48}+64 x^{8} c_1 \,\textit {\_Z}^{40}-1\right )^{56}-24 x^{8} c_1 \operatorname {RootOf}\left (x^{8} c_1 \,\textit {\_Z}^{64}+12 x^{8} c_1 \,\textit {\_Z}^{56}+48 x^{8} c_1 \,\textit {\_Z}^{48}+64 x^{8} c_1 \,\textit {\_Z}^{40}-1\right )^{48}-48 x^{8} c_1 \operatorname {RootOf}\left (x^{8} c_1 \,\textit {\_Z}^{64}+12 x^{8} c_1 \,\textit {\_Z}^{56}+48 x^{8} c_1 \,\textit {\_Z}^{48}+64 x^{8} c_1 \,\textit {\_Z}^{40}-1\right )^{40}+1}{2 c_1 \,x^{7} \operatorname {RootOf}\left (x^{8} c_1 \,\textit {\_Z}^{64}+12 x^{8} c_1 \,\textit {\_Z}^{56}+48 x^{8} c_1 \,\textit {\_Z}^{48}+64 x^{8} c_1 \,\textit {\_Z}^{40}-1\right )^{40} \left (\operatorname {RootOf}\left (x^{8} c_1 \,\textit {\_Z}^{64}+12 x^{8} c_1 \,\textit {\_Z}^{56}+48 x^{8} c_1 \,\textit {\_Z}^{48}+64 x^{8} c_1 \,\textit {\_Z}^{40}-1\right )^{16}+8 \operatorname {RootOf}\left (x^{8} c_1 \,\textit {\_Z}^{64}+12 x^{8} c_1 \,\textit {\_Z}^{56}+48 x^{8} c_1 \,\textit {\_Z}^{48}+64 x^{8} c_1 \,\textit {\_Z}^{40}-1\right )^{8}+16\right )}
\]
✓ Mathematica. Time used: 5.63 (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*} \text {Solution too large to show}\end{align*}
✓ Sympy. Time used: 0.768 (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)
\[
\log {\left (y{\left (x \right )} \right )} = C_{1} - \log {\left (\left (\frac {x}{y{\left (x \right )}} - 2\right )^{\frac {5}{8}} \left (\frac {x}{y{\left (x \right )}} + \frac {2}{3}\right )^{\frac {3}{8}} \right )}
\]