Internal problem ID [3842]
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]
\[ \boxed {\left (1+y\right ) y^{\prime } \sqrt {x^{2}+1}-y^{3}=0} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) = \frac {-1+\sqrt {1-2 c_{1} -2 \,\operatorname {arcsinh}\left (x \right )}}{2 c_{1} +2 \,\operatorname {arcsinh}\left (x \right )} y \left (x \right ) = -\frac {1+\sqrt {1-2 c_{1} -2 \,\operatorname {arcsinh}\left (x \right )}}{2 \left (\operatorname {arcsinh}\left (x \right )+c_{1} \right )} \end{align*}
✓ Solution by Mathematica
Time used: 0.621 (sec). Leaf size: 120
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+\sqrt {2 \log \left (\sqrt {x^2+1}-x\right )+1-2 c_1}}{-2 \log \left (\sqrt {x^2+1}-x\right )+2 c_1} y(x)\to \frac {-1+\sqrt {2 \log \left (\sqrt {x^2+1}-x\right )+1-2 c_1}}{2 \left (-\log \left (\sqrt {x^2+1}-x\right )+c_1\right )} y(x)\to 0 \end{align*}