Internal problem ID [9178]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 843.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-\frac {y+\ln \left (x \right )^{3} x^{3}+2 x^{3} \ln \left (x \right )^{2} y+y^{2} x^{3} \ln \left (x \right )}{x \ln \left (x \right )}=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = -\frac {\ln \left (x \right ) \left (6 x^{3} \ln \left (x \right )-2 x^{3}+9 c_{1} +18\right )}{6 x^{3} \ln \left (x \right )-2 x^{3}+9 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.378 (sec). Leaf size: 52
DSolve[y'[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*}