Internal problem ID [4577]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 24. First order differential equations. Test excercise 24. page 1067
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {y}{x}-y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 31
dsolve(diff(y(x),x)+y(x)/x=y(x)^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{\sqrt {c_{1} x^{2}+2 x}} \\ y \relax (x ) = -\frac {1}{\sqrt {c_{1} x^{2}+2 x}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.327 (sec). Leaf size: 40
DSolve[y'[x]+y[x]/x==y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {x (2+c_1 x)}} \\ y(x)\to \frac {1}{\sqrt {x (2+c_1 x)}} \\ y(x)\to 0 \\ \end{align*}