Internal problem ID [5052]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 53.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {y \left (1+\sqrt {y^{4} x^{2}-1}\right )+2 x y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (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)
\[ y \relax (x ) = \frac {\RootOf \left (-\ln \relax (x )+c_{1}-2 \left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a} \sqrt {\textit {\_a}^{4}-1}}d \textit {\_a} \right )\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.167 (sec). Leaf size: 40
DSolve[y[x]*(1+Sqrt[x^2*y[x]^4-1])+2*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\text {ArcTan}\left (\sqrt {x^2 y(x)^4-1}\right )+\frac {1}{2} \log \left (x^2 y(x)^4\right )-2 \log (y(x))=c_1,y(x)\right ] \]