Internal problem ID [3973]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 25
Problem number: 727.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{\frac {3}{2}} y^{\prime }-y^{2}=1} \]
✓ Solution by Maple
Time used: 0.078 (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)
\[ \frac {x}{\sqrt {x^{2}+1}}-\operatorname {arcsinh}\left (y \left (x \right )\right )-\frac {\ln \left (1+y \left (x \right )^{2}\right )}{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 16.191 (sec). Leaf size: 115
DSolve[(y[x]+Sqrt[1+y[x]^2])(1+x^2)^(3/2) 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*}