Internal problem ID [8595]
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]
\[ \boxed {2 x^{2} y^{\prime } y-y^{2}=x^{2} {\mathrm e}^{x -\frac {1}{x}}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 53
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 \left (x \right ) &= \sqrt {{\mathrm e}^{-\frac {1}{x}} c_{1} +{\mathrm e}^{\frac {\left (x -1\right ) \left (x +1\right )}{x}}} \\ y \left (x \right ) &= -\sqrt {{\mathrm e}^{-\frac {1}{x}} c_{1} +{\mathrm e}^{\frac {\left (x -1\right ) \left (x +1\right )}{x}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.964 (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*}