Internal problem ID [2060]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime } x +y \left (1+y^{2}\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(x*diff(y(x),x)+y(x)*(y(x)^2+1)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {1}{\sqrt {c_{1} x^{2}-1}} \\ y \left (x \right ) &= -\frac {1}{\sqrt {c_{1} x^{2}-1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.438 (sec). Leaf size: 76
DSolve[x*y'[x]+y[x]*(y[x]^2+1)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i e^{c_1}}{\sqrt {-x^2+e^{2 c_1}}} \\ y(x)\to \frac {i e^{c_1}}{\sqrt {-x^2+e^{2 c_1}}} \\ y(x)\to 0 \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}