Internal problem ID [13321]
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: 4.6 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y y^{\prime }-y^{2} x=-9 x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve(y(x)*diff(y(x),x)=x*y(x)^2-9*x,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {{\mathrm e}^{x^{2}} c_{1} +9} \\ y \left (x \right ) &= -\sqrt {{\mathrm e}^{x^{2}} c_{1} +9} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.856 (sec). Leaf size: 53
DSolve[y[x]*y'[x]==x*y[x]^2-9*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {9+e^{x^2+2 c_1}} \\ y(x)\to \sqrt {9+e^{x^2+2 c_1}} \\ y(x)\to -3 \\ y(x)\to 3 \\ \end{align*}