Internal problem ID [7877]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 297.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {2 x \left (y^{2}+5 x^{2}\right ) y^{\prime }+y^{3}-y x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.632 (sec). Leaf size: 29
dsolve(2*x*(y(x)^2+5*x^2)*diff(y(x),x)+y(x)^3-x^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (\textit {\_Z}^{45} c_{1} x^{9}-\textit {\_Z}^{18}-6 \textit {\_Z}^{9}-9\right )^{\frac {9}{2}} x \]
✓ Solution by Mathematica
Time used: 1.101 (sec). Leaf size: 216
DSolve[2*x*(y[x]^2+5*x^2)*y'[x]+y[x]^3-x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\&,1\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\&,2\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\&,3\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\&,4\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^5+\frac {\text {$\#$1}^2 e^{3 c_1}}{x^{3/2}}+3 e^{3 c_1} \sqrt {x}\&,5\right ] \\ \end{align*}