56.1.30 problem 31

Internal problem ID [8742]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 31
Date solved : Monday, January 27, 2025 at 04:46:03 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} y^{\prime }&=\frac {5 x^{2}-y x +y^{2}}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 19

dsolve(diff(y(x),x)=(5*x^2-x*y(x)+y(x)^2)/x^2,y(x), singsol=all)
 

\[ y = x \left (1+2 \tan \left (2 \ln \left (x \right )+2 c_{1} \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.899 (sec). Leaf size: 18

DSolve[D[y[x],x]==(5*x^2-x*y[x]+y[x]^2)/x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x+2 x \tan (2 (\log (x)+c_1)) \]