Internal problem ID [15167]
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: 305.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {x y^{\prime }+y-y^{2} \ln \left (x \right )=0} \] With initial conditions \begin {align*} \left [y \left (1\right ) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 11
dsolve([x*diff(y(x),x)+y(x)=y(x)^2*ln(x),y(1) = 1/2],y(x), singsol=all)
\[ y = \frac {1}{1+x +\ln \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.142 (sec). Leaf size: 12
DSolve[{x*y'[x]+y[x]==y[x]^2*Log[x],{y[1]==1/2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{x+\log (x)+1} \]