Internal problem ID [3466]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 728.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{\frac {3}{2}} y^{\prime }-1-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 28
dsolve((y(x)+sqrt(1+y(x)^2))*(x^2+1)^(3/2)*diff(y(x),x) = 1+y(x)^2,y(x), singsol=all)
\[ \frac {x}{\sqrt {x^{2}+1}}-\arcsinh \left (y \relax (x )\right )-\frac {\ln \left (1+y \relax (x )^{2}\right )}{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.388 (sec). Leaf size: 115
DSolve[(1+x^2)^(3/2) (y[x]+Sqrt[1+y[x]^2])y'[x]==1+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i \left (1+e^{\frac {x}{\sqrt {x^2+1}}+c_1}\right )}{\sqrt {1+2 e^{\frac {x}{\sqrt {x^2+1}}+c_1}}} \\ y(x)\to \frac {i \left (1+e^{\frac {x}{\sqrt {x^2+1}}+c_1}\right )}{\sqrt {1+2 e^{\frac {x}{\sqrt {x^2+1}}+c_1}}} \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}