Internal problem ID [11698]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {x^{2} y^{\prime }+y x -\frac {y^{3}}{x}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.063 (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)
\[ y \left (x \right ) = \frac {2 x}{\sqrt {2 x^{4}+2}} \]
✓ Solution by Mathematica
Time used: 0.355 (sec). Leaf size: 21
DSolve[{x^2*y'[x]+x*y[x]==y[x]^3/x,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sqrt {2} x}{\sqrt {x^4+1}} \]