Internal problem ID [3850]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 2
Problem number: 1.4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {1+y^{2}-\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{\frac {3}{2}} y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.102 (sec). Leaf size: 28
dsolve((1+y(x)^2)-(y(x)+sqrt(1+y(x)^2))*(1+x^2)^(3/2)*diff(y(x),x)=0,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: 1.721 (sec). Leaf size: 115
DSolve[(1+y[x]^2)-(y[x]+Sqrt[1+y[x]^2])*(1+x^2)^(3/2)*y'[x]==0,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*}