Internal problem ID [2596]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, section 10, page 47
Problem number: 4(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class D], _rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x -x^{5}-x^{3} y^{2}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(x*diff(y(x),x)=x^5+x^3*y(x)^2+y(x),y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\frac {x^{4}}{4}+c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.259 (sec). Leaf size: 18
DSolve[x*y'[x]==x^5+x^3*y[x]^2+y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \tan \left (\frac {x^4}{4}+c_1\right ) \\ \end{align*}