Internal problem ID [13311]
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: 4.4 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x y y^{\prime }-y^{2}=9} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(x*y(x)*diff(y(x),x)=y(x)^2+9,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {c_{1} x^{2}-9} \\ y \left (x \right ) &= -\sqrt {c_{1} x^{2}-9} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.401 (sec). Leaf size: 57
DSolve[x*y[x]*y'[x]==y[x]^2+9,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-9+e^{2 c_1} x^2} \\ y(x)\to \sqrt {-9+e^{2 c_1} x^2} \\ y(x)\to -3 i \\ y(x)\to 3 i \\ \end{align*}