Internal problem ID [3443]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 187.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x y^{\prime }-y \left (y^{2}+1\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(x*diff(y(x),x) = y(x)*(1+y(x)^2),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {x}{\sqrt {-x^{2}+c_{1}}} \\ y \left (x \right ) &= -\frac {x}{\sqrt {-x^{2}+c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.681 (sec). Leaf size: 110
DSolve[x y'[x]==y[x](1+y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i e^{c_1} x}{\sqrt {-1+e^{2 c_1} x^2}} \\ y(x)\to \frac {i e^{c_1} x}{\sqrt {-1+e^{2 c_1} x^2}} \\ y(x)\to 0 \\ y(x)\to -i \\ y(x)\to i \\ y(x)\to -\frac {i x}{\sqrt {x^2}} \\ y(x)\to \frac {i x}{\sqrt {x^2}} \\ \end{align*}