60.1.193 problem 194

Internal problem ID [10207]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 194
Date solved : Monday, January 27, 2025 at 06:38:24 PM
CAS classification : [_Riccati]

\begin{align*} x y^{\prime } \ln \left (x \right )-y^{2} \ln \left (x \right )-\left (2 \ln \left (x \right )^{2}+1\right ) y-\ln \left (x \right )^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 23

dsolve(x*diff(y(x),x)*ln(x) - y(x)^2*ln(x) - (2*ln(x)^2+1)*y(x) - ln(x)^3=0,y(x), singsol=all)
 

\[ y = -\frac {\ln \left (x \right ) \left (\ln \left (x \right )^{2}+c_{1} +2\right )}{\ln \left (x \right )^{2}+c_{1}} \]

✓ Solution by Mathematica

Time used: 0.305 (sec). Leaf size: 38

DSolve[x*D[y[x],x]*Log[x] - y[x]^2*Log[x] - (2*Log[x]^2+1)*y[x] - Log[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\log (x) \left (\log ^2(x)+2+2 c_1\right )}{\log ^2(x)+2 c_1} \\ y(x)\to -\log (x) \\ \end{align*}