20.2.10 problem Problem 10

Internal problem ID [3602]
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
Date solved : Monday, January 27, 2025 at 07:47:16 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {x^{2} y-32}{-x^{2}+16}+2 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 29

dsolve(diff(y(x),x)=(x^2*y(x)-32)/(16-x^2)+2,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{1} \left (x +4\right )^{2} {\mathrm e}^{-x}+2 \left (x -4\right )^{2}}{\left (x -4\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.183 (sec). Leaf size: 40

DSolve[D[y[x],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*}