Internal problem ID [7883]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 304.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {\left (10 y^{2} x^{3}+y x^{2}+2 x \right ) y^{\prime }+5 x^{2} y^{3}+y^{2} x=0} \]
✓ Solution by Maple
Time used: 0.188 (sec). Leaf size: 44
dsolve((10*x^3*y(x)^2+x^2*y(x)+2*x)*diff(y(x),x)+5*x^2*y(x)^3+x*y(x)^2=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\tan \left (\operatorname {RootOf}\left (\sqrt {10}\, \ln \left (\frac {4 \tan \left (\textit {\_Z} \right )^{2} \left (\tan \left (\textit {\_Z} \right )^{2}+1\right )}{5 x^{2}}\right )+2 \sqrt {10}\, c_{1} +2 \textit {\_Z} \right )\right ) \sqrt {10}}{5 x} \]
✓ Solution by Mathematica
Time used: 0.296 (sec). Leaf size: 44
DSolve[(10*x^3*y[x]^2+x^2*y[x]+2*x)*y'[x]+5*x^2*y[x]^3+x*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [y(x) \sqrt {5 x^2 y(x)^2+2} e^{\frac {\arctan \left (\sqrt {\frac {5}{2}} x y(x)\right )}{\sqrt {10}}}=c_1,y(x)\right ] \]