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
:
Monday, January 27, 2025 at 02:03:18 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*}
✓ Solution by Maple
Time used: 0.164 (sec). Leaf size: 278
dsolve(y(x)-3*x+(4*y(x)+3*x)*diff(y(x),x)=0,y(x), singsol=all)
\[
y = \frac {-3 x^{8} c_1 \operatorname {RootOf}\left (x^{8} c_1 \,\textit {\_Z}^{64}+12 x^{8} c_1 \,\textit {\_Z}^{56}+48 x^{8} c_1 \,\textit {\_Z}^{48}+64 x^{8} c_1 \,\textit {\_Z}^{40}-1\right )^{56}-24 x^{8} c_1 \operatorname {RootOf}\left (x^{8} c_1 \,\textit {\_Z}^{64}+12 x^{8} c_1 \,\textit {\_Z}^{56}+48 x^{8} c_1 \,\textit {\_Z}^{48}+64 x^{8} c_1 \,\textit {\_Z}^{40}-1\right )^{48}-48 x^{8} c_1 \operatorname {RootOf}\left (x^{8} c_1 \,\textit {\_Z}^{64}+12 x^{8} c_1 \,\textit {\_Z}^{56}+48 x^{8} c_1 \,\textit {\_Z}^{48}+64 x^{8} c_1 \,\textit {\_Z}^{40}-1\right )^{40}+1}{2 c_1 \,x^{7} \operatorname {RootOf}\left (x^{8} c_1 \,\textit {\_Z}^{64}+12 x^{8} c_1 \,\textit {\_Z}^{56}+48 x^{8} c_1 \,\textit {\_Z}^{48}+64 x^{8} c_1 \,\textit {\_Z}^{40}-1\right )^{40} \left (\operatorname {RootOf}\left (x^{8} c_1 \,\textit {\_Z}^{64}+12 x^{8} c_1 \,\textit {\_Z}^{56}+48 x^{8} c_1 \,\textit {\_Z}^{48}+64 x^{8} c_1 \,\textit {\_Z}^{40}-1\right )^{16}+8 \operatorname {RootOf}\left (x^{8} c_1 \,\textit {\_Z}^{64}+12 x^{8} c_1 \,\textit {\_Z}^{56}+48 x^{8} c_1 \,\textit {\_Z}^{48}+64 x^{8} c_1 \,\textit {\_Z}^{40}-1\right )^{8}+16\right )}
\]
✓ Solution by Mathematica
Time used: 5.630 (sec). Leaf size: 673
DSolve[y[x]-3*x+(4*y[x]+3*x)*D[y[x],x]==0,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*}