Internal problem ID [5085]
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]
\[ \boxed {y^{\prime }+\frac {y}{x}-y^{3}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x)+y(x)/x=y(x)^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {1}{\sqrt {x \left (c_{1} x +2\right )}} \\ y \left (x \right ) &= -\frac {1}{\sqrt {x \left (c_{1} x +2\right )}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.375 (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*}