73.5.20 problem 6.7 (h)

Internal problem ID [15131]
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)
Date solved : Tuesday, January 28, 2025 at 07:36:04 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} y^{\prime }+\frac {y}{x}&=x^{2} y^{3} \end{align*}

✓ Solution by Maple

Time used: 0.003 (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: 0.429 (sec). Leaf size: 44

DSolve[D[y[x],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*}