64.6.12 problem 12

Internal problem ID [13362]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 05:32:05 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(x^2*diff(y(x),x)+x*y(x)=x*y(x)^3,y(x), singsol=all)
 

\begin{align*} y &= \frac {1}{\sqrt {c_{1} x^{2}+1}} \\ y &= -\frac {1}{\sqrt {c_{1} x^{2}+1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.372 (sec). Leaf size: 52

DSolve[x^2*D[y[x],x]+x*y[x]==x*y[x]^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) K[1] (K[1]+1)}dK[1]\&\right ][\log (x)+c_1] \\ y(x)\to -1 \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}