Internal problem ID [1986]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number: Problem 14.6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {2 x^{2}+y^{2}+x}{y x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 49
dsolve(diff(y(x),x) = - (2*x^2+y(x)^2+x)/(x*y(x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {-9 x^{4}-6 x^{3}+9 c_{1}}}{3 x} \\ y \relax (x ) = \frac {\sqrt {-9 x^{4}-6 x^{3}+9 c_{1}}}{3 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.248 (sec). Leaf size: 56
DSolve[y'[x] == - (2*x^2+y[x]^2+x)/(x*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-\frac {1}{3} x^3 (3 x+2)+c_1}}{x} \\ y(x)\to \frac {\sqrt {-\frac {1}{3} x^3 (3 x+2)+c_1}}{x} \\ \end{align*}