29.19.19 problem 532
Internal
problem
ID
[5128]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
19
Problem
number
:
532
Date
solved
:
Monday, January 27, 2025 at 10:13:20 AM
CAS
classification
:
[[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\begin{align*} x \left (y+2 x \right ) y^{\prime }&=x^{2}+y x -y^{2} \end{align*}
✓ Solution by Maple
Time used: 0.928 (sec). Leaf size: 59
dsolve(x*(2*x+y(x))*diff(y(x),x) = x^2+x*y(x)-y(x)^2,y(x), singsol=all)
\[
y \left (x \right ) = \frac {x \left (\operatorname {RootOf}\left (3 \textit {\_Z}^{15}+\textit {\_Z}^{9}-2 c_{1} x^{3}\right )^{9}+c_{1} x^{3}\right )}{-\operatorname {RootOf}\left (3 \textit {\_Z}^{15}+\textit {\_Z}^{9}-2 c_{1} x^{3}\right )^{9}+2 c_{1} x^{3}}
\]
✓ Solution by Mathematica
Time used: 4.831 (sec). Leaf size: 431
DSolve[x(2 x+y[x])D[y[x],x]==x^2+x y[x]-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*}
y(x)\to \text {Root}\left [32 \text {$\#$1}^5-80 \text {$\#$1}^4 x+80 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (-40 x^3+\frac {e^{6 c_1}}{x^3}\right )+\text {$\#$1} \left (10 x^4+\frac {2 e^{6 c_1}}{x^2}\right )-x^5+\frac {e^{6 c_1}}{x}\&,1\right ] \\
y(x)\to \text {Root}\left [32 \text {$\#$1}^5-80 \text {$\#$1}^4 x+80 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (-40 x^3+\frac {e^{6 c_1}}{x^3}\right )+\text {$\#$1} \left (10 x^4+\frac {2 e^{6 c_1}}{x^2}\right )-x^5+\frac {e^{6 c_1}}{x}\&,2\right ] \\
y(x)\to \text {Root}\left [32 \text {$\#$1}^5-80 \text {$\#$1}^4 x+80 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (-40 x^3+\frac {e^{6 c_1}}{x^3}\right )+\text {$\#$1} \left (10 x^4+\frac {2 e^{6 c_1}}{x^2}\right )-x^5+\frac {e^{6 c_1}}{x}\&,3\right ] \\
y(x)\to \text {Root}\left [32 \text {$\#$1}^5-80 \text {$\#$1}^4 x+80 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (-40 x^3+\frac {e^{6 c_1}}{x^3}\right )+\text {$\#$1} \left (10 x^4+\frac {2 e^{6 c_1}}{x^2}\right )-x^5+\frac {e^{6 c_1}}{x}\&,4\right ] \\
y(x)\to \text {Root}\left [32 \text {$\#$1}^5-80 \text {$\#$1}^4 x+80 \text {$\#$1}^3 x^2+\text {$\#$1}^2 \left (-40 x^3+\frac {e^{6 c_1}}{x^3}\right )+\text {$\#$1} \left (10 x^4+\frac {2 e^{6 c_1}}{x^2}\right )-x^5+\frac {e^{6 c_1}}{x}\&,5\right ] \\
\end{align*}