Internal problem ID [1954]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 8, page 34
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\frac {2}{y}-\frac {y}{x^{2}}+\left (\frac {1}{x}-\frac {2 x}{y^{2}}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 54
dsolve((2/y(x)-y(x)/x^2)+(1/x-2*x/y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y = \sqrt {2}\, x y = -\sqrt {2}\, x y = \left (-\frac {c_{1}}{2}-\frac {\sqrt {c_{1}^{2}-8}}{2}\right ) x y = \left (-\frac {c_{1}}{2}+\frac {\sqrt {c_{1}^{2}-8}}{2}\right ) x \end{align*}
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 55
DSolve[(2/y[x]-y[x]/x^2)+(1/x-2*x/y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2} x y(x)\to \sqrt {2} x y(x)\to c_1 x y(x)\to -\sqrt {2} x y(x)\to \sqrt {2} x \end{align*}