Internal problem ID [2631]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 1, First-Order Differential Equations. Section 1.4, Separable Differential
Equations. page 43
Problem number: Problem 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {y x^{2}-32}{-x^{2}+16}=2} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(x),x)=(x^2*y(x)-32)/(16-x^2)+2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-x} \left (x^{2}+8 x +16\right ) c_{1}}{\left (x -4\right )^{2}}+2 \,{\mathrm e}^{-x} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.148 (sec). Leaf size: 40
DSolve[y'[x]==(x^2*y[x]-32)/(16-x^2)+2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-x} \left (2 e^x (x-4)^2+c_1 (x+4)^2\right )}{(x-4)^2} y(x)\to 2 \end{align*}