Internal problem ID [4601]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 24. First order differential equations. Further problems 24. page 1068
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {2 y^{\prime }+y-y^{3} \left (x -1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 25
dsolve(2*diff(y(x),x)+y(x)=y(x)^3*(x-1),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{\sqrt {c_{1} {\mathrm e}^{x}+x}} \\ y \relax (x ) = -\frac {1}{\sqrt {c_{1} {\mathrm e}^{x}+x}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.342 (sec). Leaf size: 40
DSolve[2*y'[x]+y[x]==y[x]^3*(x-1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {x+c_1 e^x}} \\ y(x)\to \frac {1}{\sqrt {x+c_1 e^x}} \\ y(x)\to 0 \\ \end{align*}