Internal problem ID [3334]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 592.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (1+y\right ) y^{\prime } \sqrt {x^{2}+1}-y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 49
dsolve((1+y(x))*diff(y(x),x)*sqrt(x^2+1) = y(x)^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-1+\sqrt {1-2 c_{1}-2 \arcsinh \relax (x )}}{2 \arcsinh \relax (x )+2 c_{1}} \\ y \relax (x ) = -\frac {1+\sqrt {1-2 c_{1}-2 \arcsinh \relax (x )}}{2 \left (\arcsinh \relax (x )+c_{1}\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.88 (sec). Leaf size: 72
DSolve[(1+y[x])y'[x]Sqrt[1+x^2]==y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{-1+\sqrt {-2 \tanh ^{-1}\left (\frac {x}{\sqrt {x^2+1}}\right )+1-2 c_1}} \\ y(x)\to -\frac {1}{1+\sqrt {-2 \tanh ^{-1}\left (\frac {x}{\sqrt {x^2+1}}\right )+1-2 c_1}} \\ y(x)\to 0 \\ \end{align*}