60.2.267 problem 843

Internal problem ID [10854]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 843
Date solved : Monday, January 27, 2025 at 10:15:33 PM
CAS classification : [_Riccati]

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

✓ Solution by Maple

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

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

\[ y = -\frac {\ln \left (x \right ) \left (6 x^{3} \ln \left (x \right )-2 x^{3}+9 c_{1} +18\right )}{6 x^{3} \ln \left (x \right )-2 x^{3}+9 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.333 (sec). Leaf size: 52

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

\begin{align*} y(x)\to \frac {\log (x) \left (x^3-3 x^3 \log (x)-9 (1+c_1)\right )}{-x^3+3 x^3 \log (x)+9 c_1} \\ y(x)\to -\log (x) \\ \end{align*}