Internal problem ID [15163]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 12. Miscellaneous problems. Exercises page 93
Problem number: 301.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {4 y x^{3}-2 y^{2} x +\left (y^{2}+2 y x^{2}-x^{4}\right ) y^{\prime }=-2 x^{5}} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 53
dsolve(2*(x^5+2*x^3*y(x)-y(x)^2*x)+(y(x)^2+2*x^2*y(x)-x^4)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y &= \frac {c_{1}}{2}-\frac {\sqrt {-4 x^{4}+4 c_{1} x^{2}+c_{1}^{2}}}{2} \\ y &= \frac {c_{1}}{2}+\frac {\sqrt {-4 x^{4}+4 c_{1} x^{2}+c_{1}^{2}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 15.349 (sec). Leaf size: 87
DSolve[2*(x^5+2*x^3*y[x]-y[x]^2*x)+(y[x]^2+2*x^2*y[x]-x^4)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (e^{2 c_1}-\sqrt {-4 x^4+4 e^{2 c_1} x^2+e^{4 c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {-4 x^4+4 e^{2 c_1} x^2+e^{4 c_1}}+e^{2 c_1}\right ) \\ \end{align*}