Internal problem ID [7749]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 170.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Riccati]
\[ \boxed {y^{\prime } x^{3}-y^{2}-x^{4}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve(x^3*diff(y(x),x) - y(x)^2 - x^4=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{2} \left (\ln \left (x \right )-c_{1} -1\right )}{\ln \left (x \right )-c_{1}} \]
✓ Solution by Mathematica
Time used: 0.156 (sec). Leaf size: 27
DSolve[x^3*y'[x] - y[x]^2 - x^4==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 \left (1-\frac {1}{\log (x)+c_1}\right ) \\ y(x)\to x^2 \\ \end{align*}