Internal problem ID [13345]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page
90
Problem number: 4.8 (f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {y^{2}-1}{y x}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 15
dsolve([diff(y(x),x)=(y(x)^2-1)/(x*y(x)),y(1) = -2],y(x), singsol=all)
\[ y \left (x \right ) = -\sqrt {3 x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.248 (sec). Leaf size: 18
DSolve[{y'[x]==(y[x]^2-1)/(x*y[x]),{y[1]==-2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\sqrt {3 x^2+1} \]