56.1.16 problem 16
Internal
problem
ID
[8728]
Book
:
Own
collection
of
miscellaneous
problems
Section
:
section
1.0
Problem
number
:
16
Date
solved
:
Monday, January 27, 2025 at 04:20:49 PM
CAS
classification
:
[[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\begin{align*} y^{\prime }&=\frac {-y x -1}{4 x^{3} y-2 x^{2}} \end{align*}
✓ Solution by Maple
Time used: 1.770 (sec). Leaf size: 37
dsolve(diff(y(x),x)=(-x*y(x)-1)/(4*x^3*y(x)-2*x^2),y(x), singsol=all)
\[
y = \frac {\operatorname {RootOf}\left (\textit {\_Z}^{25} c_{1} -10 \textit {\_Z}^{20} c_{1} +25 \textit {\_Z}^{15} c_{1} -16 x^{5}\right )^{5}-1}{4 x}
\]
✓ Solution by Mathematica
Time used: 14.178 (sec). Leaf size: 391
DSolve[D[y[x],x] == (-x*y[x]-1)/(4*x^3*y[x]-2*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*}
y(x)\to \text {Root}\left [64 \text {$\#$1}^5 c_1{}^5 x^5-80 \text {$\#$1}^4 c_1{}^5 x^4-20 \text {$\#$1}^3 c_1{}^5 x^3+25 \text {$\#$1}^2 c_1{}^5 x^2+10 \text {$\#$1} c_1{}^5 x-x^5+c_1{}^5\&,1\right ] \\
y(x)\to \text {Root}\left [64 \text {$\#$1}^5 c_1{}^5 x^5-80 \text {$\#$1}^4 c_1{}^5 x^4-20 \text {$\#$1}^3 c_1{}^5 x^3+25 \text {$\#$1}^2 c_1{}^5 x^2+10 \text {$\#$1} c_1{}^5 x-x^5+c_1{}^5\&,2\right ] \\
y(x)\to \text {Root}\left [64 \text {$\#$1}^5 c_1{}^5 x^5-80 \text {$\#$1}^4 c_1{}^5 x^4-20 \text {$\#$1}^3 c_1{}^5 x^3+25 \text {$\#$1}^2 c_1{}^5 x^2+10 \text {$\#$1} c_1{}^5 x-x^5+c_1{}^5\&,3\right ] \\
y(x)\to \text {Root}\left [64 \text {$\#$1}^5 c_1{}^5 x^5-80 \text {$\#$1}^4 c_1{}^5 x^4-20 \text {$\#$1}^3 c_1{}^5 x^3+25 \text {$\#$1}^2 c_1{}^5 x^2+10 \text {$\#$1} c_1{}^5 x-x^5+c_1{}^5\&,4\right ] \\
y(x)\to \text {Root}\left [64 \text {$\#$1}^5 c_1{}^5 x^5-80 \text {$\#$1}^4 c_1{}^5 x^4-20 \text {$\#$1}^3 c_1{}^5 x^3+25 \text {$\#$1}^2 c_1{}^5 x^2+10 \text {$\#$1} c_1{}^5 x-x^5+c_1{}^5\&,5\right ] \\
\end{align*}