Internal problem ID [3986]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 745.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {\left (1-2 x -\ln \left (y\right )\right ) y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve((1-2*x-ln(y(x)))*diff(y(x),x)+2*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\operatorname {LambertW}\left (-2 \,{\mathrm e}^{-2 x} c_{1} \right )}{2 c_{1}} \]
✓ Solution by Mathematica
Time used: 60.223 (sec). Leaf size: 23
DSolve[(1-2 x -Log[y[x]])y'[x]+2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {W\left (-2 c_1 e^{-2 x}\right )}{2 c_1} \]