Internal problem ID [7750]
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]
Solve \begin {gather*} \boxed {x^{3} y^{\prime }-y^{2}-x^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 23
dsolve(x^3*diff(y(x),x) - y(x)^2 - x^4=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2} \left (\ln \relax (x )-c_{1}-1\right )}{\ln \relax (x )-c_{1}} \]
✓ Solution by Mathematica
Time used: 0.155 (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*}