Internal problem ID [3494]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 238.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {2 x y^{\prime }-y \left (y^{2}+1\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(2*x*diff(y(x),x) = y(x)*(1+y(x)^2),y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {\sqrt {\left (c_{1} -x \right ) x}}{c_{1} -x} y \left (x \right ) = -\frac {\sqrt {\left (c_{1} -x \right ) x}}{c_{1} -x} \end{align*}
✓ Solution by Mathematica
Time used: 0.534 (sec). Leaf size: 82
DSolve[2 x y'[x]==y[x](1+y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i e^{c_1} \sqrt {x}}{\sqrt {-1+e^{2 c_1} x}} y(x)\to \frac {i e^{c_1} \sqrt {x}}{\sqrt {-1+e^{2 c_1} x}} y(x)\to 0 y(x)\to -i y(x)\to i \end{align*}