Internal problem ID [13075]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number: 6.7 (h).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {y^{\prime }+\frac {y}{x}-y^{3} x^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x)+1/x*y(x)=x^2*y(x)^3,y(x), singsol=all)
\begin{align*} y = \frac {1}{\sqrt {c_{1} -2 x}\, x} y = -\frac {1}{\sqrt {c_{1} -2 x}\, x} \end{align*}
✓ Solution by Mathematica
Time used: 0.336 (sec). Leaf size: 44
DSolve[y'[x]+1/x*y[x]==x^2*y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {x^2 (-2 x+c_1)}} y(x)\to \frac {1}{\sqrt {x^2 (-2 x+c_1)}} y(x)\to 0 \end{align*}