75.5.3 problem 102

Internal problem ID [16739]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 5. Homogeneous equations. Exercises page 44
Problem number : 102
Date solved : Tuesday, January 28, 2025 at 09:20:25 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.075 (sec). Leaf size: 13

dsolve(x*diff(y(x),x)=y(x)*( ln(y(x))-ln(x) ),y(x), singsol=all)
 

\[ y = x \,{\mathrm e}^{-c_{1} x +1} \]

✓ Solution by Mathematica

Time used: 0.238 (sec). Leaf size: 24

DSolve[x*D[y[x],x]==y[x]*( Log[y[x]]-Log[x] ),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x e^{1+e^{c_1} x} \\ y(x)\to e x \\ \end{align*}