Internal problem ID [3276]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 19
Problem number: 532.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {x \left (2 x +y\right ) y^{\prime }-x^{2}-y x +y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 63
dsolve(x*(2*x+y(x))*diff(y(x),x) = x^2+x*y(x)-y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = -\frac {x \left (-\RootOf \left (3 \textit {\_Z}^{15}+\textit {\_Z}^{9}-2 x^{3} c_{1}\right )^{9}-x^{3} c_{1}\right )}{-\RootOf \left (3 \textit {\_Z}^{15}+\textit {\_Z}^{9}-2 x^{3} c_{1}\right )^{9}+2 x^{3} c_{1}} \]
✓ Solution by Mathematica
Time used: 4.236 (sec). Leaf size: 431
DSolve[x(2 x+y[x])y'[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*}