Internal problem ID [13387]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number: 6.6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _rational, _Bernoulli]
\[ \boxed {y^{\prime }-\frac {y}{x}-\frac {1}{y}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 13
dsolve([diff(y(x),x)-1/x*y(x)=1/y(x),y(1) = 3],y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {x \left (11 x -2\right )} \]
✓ Solution by Mathematica
Time used: 0.251 (sec). Leaf size: 20
DSolve[{y'[x]-1/x*y[x]==1/y[x],{y[1]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {x} \sqrt {11 x-2} \]