Internal problem ID [14980]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 4. Equations with variables separable and equations reducible to them. Exercises
page 38
Problem number: 53.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\ln \left (y\right ) y+y^{\prime } x=1} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.922 (sec). Leaf size: 38
dsolve([y(x)*ln(y(x))+x*diff(y(x),x)=1,y(1) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {RootOf}\left (\int _{1}^{\textit {\_Z}}\frac {1}{\ln \left (\textit {\_a} \right ) \textit {\_a} -1}d \textit {\_a} +\ln \left (x \right )\right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y[x]*Log[y[x]]+x*y'[x]==1,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
{}