64.1.6 problem 2(b)

Internal problem ID [13251]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number : 2(b)
Date solved : Tuesday, January 28, 2025 at 05:13:09 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 30

dsolve(x*diff(y(x),x)+y(x)=x^3*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: 0.472 (sec). Leaf size: 44

DSolve[x*D[y[x],x]+y[x]==x^3*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*}