Internal problem ID [3216]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 74.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
\[ \boxed {y \left (6 y^{2}-x -1\right )+2 x y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 54
dsolve(y(x)*(6*y(x)^2-x-1)+2*x*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\sqrt {\left ({\mathrm e}^{-x} c_{1} +6\right ) x}}{{\mathrm e}^{-x} c_{1} +6} \\ y \left (x \right ) &= -\frac {\sqrt {\left ({\mathrm e}^{-x} c_{1} +6\right ) x}}{{\mathrm e}^{-x} c_{1} +6} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.709 (sec). Leaf size: 65
DSolve[y[x]*(6*y[x]^2-x-1)+2*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{x/2} \sqrt {x}}{\sqrt {6 e^x+c_1}} \\ y(x)\to \frac {e^{x/2} \sqrt {x}}{\sqrt {6 e^x+c_1}} \\ y(x)\to 0 \\ \end{align*}