44.6.20 problem 20

Internal problem ID [7164]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 20
Date solved : Tuesday, February 04, 2025 at 12:43:02 AM
CAS classification : [_linear]

\begin{align*} \left (x +2\right )^{2} y^{\prime }&=5-8 y-4 y x \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve((x+2)^2*diff(y(x),x)=5-8*y(x)-4*x*y(x),y(x), singsol=all)
 

\[ y = \frac {\frac {5 \left (x +2\right )^{3}}{3}+c_1}{\left (x +2\right )^{4}} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 32

DSolve[(x+2)^2*D[y[x],x]==5-8*y[x]-4*x*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {5 x^3+30 x^2+60 x+3 c_1}{3 (x+2)^4} \]