60.2.266 problem 842

Internal problem ID [10853]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 842
Date solved : Monday, January 27, 2025 at 10:15:26 PM
CAS classification : [_Riccati]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 43

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

\[ y = -\frac {\ln \left (x \right ) \left (2 \ln \left (x \right ) x^{2}-x^{2}+2 c_{1} +4\right )}{2 \ln \left (x \right ) x^{2}-x^{2}+2 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.318 (sec). Leaf size: 52

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

\begin{align*} y(x)\to \frac {\log (x) \left (x^2-2 x^2 \log (x)-4 (1+c_1)\right )}{-x^2+2 x^2 \log (x)+4 c_1} \\ y(x)\to -\log (x) \\ \end{align*}