Internal problem ID [7839]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 259.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {2 x^{2} y y^{\prime }-y^{2}-x^{2} {\mathrm e}^{x -\frac {1}{x}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 51
dsolve(2*x^2*y(x)*diff(y(x),x)-y(x)^2-x^2*exp(x-1/x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {{\mathrm e}^{-\frac {1}{x}} c_{1}+{\mathrm e}^{\frac {x^{2}-1}{x}}} \\ y \relax (x ) = -\sqrt {{\mathrm e}^{-\frac {1}{x}} c_{1}+{\mathrm e}^{\frac {x^{2}-1}{x}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.43 (sec). Leaf size: 50
DSolve[2*x^2*y[x]*y'[x]-y[x]^2-x^2*Exp[x-1/x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{\left .-\frac {1}{2}\right /x} \sqrt {e^x+c_1} \\ y(x)\to e^{\left .-\frac {1}{2}\right /x} \sqrt {e^x+c_1} \\ \end{align*}