44.6.31 problem 31

Internal problem ID [7175]
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 : 31
Date solved : Tuesday, February 04, 2025 at 12:44:13 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+y&=4 x +1 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=8 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 14

dsolve([x*diff(y(x),x)+y(x)=4*x+1,y(1) = 8],y(x), singsol=all)
 

\[ y = 2 x +\frac {5}{x}+1 \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 15

DSolve[{x*D[y[x],x]+y[x]==4*x+1,{y[1]==8}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 x+\frac {5}{x}+1 \]