Internal problem ID [1871]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 5, page 21
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x y^{2}+\left (y-x^{2} y\right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve((x*y(x)^2+x)+(y(x)-x^2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {c_{1} x^{2}-c_{1} -1} \\ y \left (x \right ) &= -\sqrt {c_{1} x^{2}-c_{1} -1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.353 (sec). Leaf size: 61
DSolve[(x*y[x]^2+x)+(y[x]-x^2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-1+e^{2 c_1} \left (x^2-1\right )} \\ y(x)\to \sqrt {-1+e^{2 c_1} \left (x^2-1\right )} \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}