Internal problem ID [7747]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 167.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Riccati]
Solve \begin {gather*} \boxed {3 y^{\prime } x^{2}-7 y^{2}-3 y x -x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 20
dsolve(3*x^2*diff(y(x),x) - 7*y(x)^2 - 3*x*y(x) - x^2=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (\frac {\left (c_{1}+\ln \relax (x )\right ) \sqrt {7}}{3}\right ) x \sqrt {7}}{7} \]
✓ Solution by Mathematica
Time used: 0.409 (sec). Leaf size: 29
DSolve[3*x^2*y'[x] - 7*y[x]^2 - 3*x*y[x] - x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x \tan \left (\frac {1}{3} \sqrt {7} (\log (x)+3 c_1)\right )}{\sqrt {7}} \\ \end{align*}