Internal problem ID [15097]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 8. First order not solved for the derivative. Exercises page 67
Problem number: 209.
ODE order: 1.
ODE degree: 0.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }={\mathrm e}^{\frac {y^{\prime }}{y}}} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 25
dsolve(diff(y(x),x)=exp(diff(y(x),x)/y(x)),y(x), singsol=all)
\[ y \left (x \right ) = -\operatorname {LambertW}\left (c_{1} {\mathrm e}^{-x}\right ) {\mathrm e}^{-\frac {1}{\operatorname {LambertW}\left (c_{1} {\mathrm e}^{-x}\right )}} \]
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 33
DSolve[y'[x]==Exp[y'[x]/y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \text {InverseFunction}\left [\frac {1}{W\left (-\frac {1}{\text {$\#$1}}\right )}-\log \left (W\left (-\frac {1}{\text {$\#$1}}\right )\right )\&\right ][-x+c_1] \]