Internal problem ID [15025]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 5. Homogeneous equations. Exercises page 44
Problem number: 118.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`]]
\[ \boxed {y \left (1+\sqrt {y^{4} x^{2}+1}\right )+2 y^{\prime } x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(y(x)*(1+sqrt(x^2*y(x)^4+1))+2*x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (-\ln \left (x \right )+c_{1} -2 \left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a} \sqrt {\textit {\_a}^{4}+1}}d \textit {\_a} \right )\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.624 (sec). Leaf size: 80
DSolve[y[x]*(1+Sqrt[x^2*y[x]^4+1])+2*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i \sqrt {2} e^{\frac {c_1}{2}}}{\sqrt {-x^2+e^{2 c_1}}} \\ y(x)\to \frac {i \sqrt {2} e^{\frac {c_1}{2}}}{\sqrt {-x^2+e^{2 c_1}}} \\ y(x)\to 0 \\ \end{align*}