Internal problem ID [11662]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number: 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {y^{\prime }+\frac {y}{2 x}-\frac {x}{y^{3}}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 17
dsolve([diff(y(x),x)+y(x)/(2*x)=x/y(x)^3,y(1) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {\frac {\sqrt {x^{4}+15}}{x}} \]
✓ Solution by Mathematica
Time used: 0.277 (sec). Leaf size: 20
DSolve[{y'[x]+y[x]/(2*x)==x/y[x]^3,{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sqrt [4]{x^4+15}}{\sqrt {x}} \]