Internal problem ID [3551]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 11
Problem number: 295.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime }-y^{2}=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 9
dsolve((x^2+1)*diff(y(x),x) = 1+y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (\arctan \left (x \right )+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.237 (sec). Leaf size: 25
DSolve[(1+x^2)y'[x]==(1+y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan (\arctan (x)+c_1) y(x)\to -i y(x)\to i \end{align*}