Internal problem ID [1889]
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: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{2}+y y^{\prime }+y^{\prime } x^{2} y=1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve(y(x)^2+y(x)*diff(y(x),x)+x^2*y(x)*diff(y(x),x)-1=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {{\mathrm e}^{-2 \arctan \left (x \right )} c_{1} +1} \\ y \left (x \right ) &= -\sqrt {{\mathrm e}^{-2 \arctan \left (x \right )} c_{1} +1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.923 (sec). Leaf size: 55
DSolve[y[x]^2+y[x]*y'[x]+x^2*y[x]*y'[x]-1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {1+e^{-2 \arctan (x)+2 c_1}} \\ y(x)\to \sqrt {1+e^{-2 \arctan (x)+2 c_1}} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}