Internal problem ID [6320]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 31.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Riccati]
\[ \boxed {y^{\prime }-\frac {5 x^{2}-y x +y^{2}}{x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(y(x),x)=(5*x^2-x*y(x)+y(x)^2)/x^2,y(x), singsol=all)
\[ y \left (x \right ) = 2 \tan \left (2 \ln \left (x \right )+2 c_{1} \right ) x +x \]
✓ Solution by Mathematica
Time used: 0.737 (sec). Leaf size: 18
DSolve[y'[x]==(5*x^2-x*y[x]+y[x]^2)/x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+2 x \tan (2 (\log (x)+c_1)) \\ \end{align*}