75.12.31 problem 305

Internal problem ID [16897]
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
Date solved : Tuesday, January 28, 2025 at 09:40:07 AM
CAS classification : [_Bernoulli]

\begin{align*} x y^{\prime }+y&=y^{2} \ln \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.043 (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: 0.153 (sec). Leaf size: 12

DSolve[{x*D[y[x],x]+y[x]==y[x]^2*Log[x],{y[1]==1/2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{x+\log (x)+1} \]