Internal problem ID [3453]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 715.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {\left (x^{2}-y^{5}\right ) y^{\prime }-2 y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 25
dsolve((x^2-y(x)^5)*diff(y(x),x) = 2*x*y(x),y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (x^{8} \textit {\_Z}^{5}+4-{\mathrm e}^{\frac {8 c_{1}}{5}} \textit {\_Z} \right ) x^{2} \]
✓ Solution by Mathematica
Time used: 1.773 (sec). Leaf size: 121
DSolve[(x^2-y[x]^5)y'[x]==2 x y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Root}\left [\text {$\#$1}^5+4 \text {$\#$1} c_1+4 x^2\&,1\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+4 \text {$\#$1} c_1+4 x^2\&,2\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+4 \text {$\#$1} c_1+4 x^2\&,3\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+4 \text {$\#$1} c_1+4 x^2\&,4\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+4 \text {$\#$1} c_1+4 x^2\&,5\right ] \\ y(x)\to 0 \\ \end{align*}