Internal problem ID [15147]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 12. Miscellaneous problems. Exercises page 93
Problem number: 285.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Bernoulli]
\[ \boxed {y^{\prime } y x -y^{2}=x^{4}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(x*y(x)*diff(y(x),x)-y(x)^2=x^4,y(x), singsol=all)
\begin{align*} y &= \sqrt {x^{2}+c_{1}}\, x \\ y &= -\sqrt {x^{2}+c_{1}}\, x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 34
DSolve[x*y[x]*y'[x]-y[x]^2==x^4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \sqrt {x^2+c_1} \\ y(x)\to x \sqrt {x^2+c_1} \\ \end{align*}