64.6.24 problem 24

Internal problem ID [13374]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 05:33:21 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.088 (sec). Leaf size: 16

dsolve([x^2*diff(y(x),x)+x*y(x)=y(x)^3/x,y(1) = 1],y(x), singsol=all)
 

\[ y = \frac {2 x}{\sqrt {2 x^{4}+2}} \]

✓ Solution by Mathematica

Time used: 0.529 (sec). Leaf size: 21

DSolve[{x^2*D[y[x],x]+x*y[x]==y[x]^3/x,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sqrt {2} x}{\sqrt {x^4+1}} \]