Internal problem ID [15154]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 12. Miscellaneous problems. Exercises page 93
Problem number: 292.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _dAlembert]
\[ \boxed {{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }=-1} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.312 (sec). Leaf size: 21
dsolve([(1+exp(x/y(x)))+(exp(x/y(x))*(1-x/y(x)))*diff(y(x),x)=0,y(1) = 1],y(x), singsol=all)
\[ y = -\frac {x}{\operatorname {LambertW}\left (\frac {x}{-1+x -{\mathrm e}}\right )} \]
✓ Solution by Mathematica
Time used: 1.228 (sec). Leaf size: 21
DSolve[{(1+Exp[x/y[x]])+(Exp[x/y[x]]*(1-x/y[x]))*y'[x]==0,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x}{W\left (\frac {x}{x-e-1}\right )} \]