60.2.417 problem 994

Internal problem ID [11004]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 994
Date solved : Monday, January 27, 2025 at 10:40:10 PM
CAS classification : [_Riccati]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 43

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

\[ y = -\frac {\ln \left (x \right ) \left (4 \ln \left (x \right ) x^{4}-x^{4}+8 c_{1} +16\right )}{4 \ln \left (x \right ) x^{4}-x^{4}+8 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.339 (sec). Leaf size: 52

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

\begin{align*} y(x)\to \frac {\log (x) \left (x^4-4 x^4 \log (x)-16 (1+c_1)\right )}{-x^4+4 x^4 \log (x)+16 c_1} \\ y(x)\to -\log (x) \\ \end{align*}