Internal problem ID [3292]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 548.
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 (x +2 y\right ) y^{\prime }+\left (2 x -y\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 33
dsolve(x*(x+2*y(x))*diff(y(x),x)+(2*x-y(x))*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\RootOf \left (\textit {\_Z}^{18}+3 \textit {\_Z}^{3} x^{3} c_{1}-x^{3} c_{1}\right )^{15}}{c_{1} x^{2}} \]
✓ Solution by Mathematica
Time used: 2.965 (sec). Leaf size: 385
DSolve[x(x+2 y[x])y'[x]+(2 x-y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Root}\left [\text {$\#$1}^6+15 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+270 \text {$\#$1}^3 x^3+405 \text {$\#$1}^2 x^4+243 \text {$\#$1} x^5-e^{3 c_1} x^3\&,1\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^6+15 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+270 \text {$\#$1}^3 x^3+405 \text {$\#$1}^2 x^4+243 \text {$\#$1} x^5-e^{3 c_1} x^3\&,2\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^6+15 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+270 \text {$\#$1}^3 x^3+405 \text {$\#$1}^2 x^4+243 \text {$\#$1} x^5-e^{3 c_1} x^3\&,3\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^6+15 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+270 \text {$\#$1}^3 x^3+405 \text {$\#$1}^2 x^4+243 \text {$\#$1} x^5-e^{3 c_1} x^3\&,4\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^6+15 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+270 \text {$\#$1}^3 x^3+405 \text {$\#$1}^2 x^4+243 \text {$\#$1} x^5-e^{3 c_1} x^3\&,5\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^6+15 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+270 \text {$\#$1}^3 x^3+405 \text {$\#$1}^2 x^4+243 \text {$\#$1} x^5-e^{3 c_1} x^3\&,6\right ] \\ \end{align*}