44.1.25 problem 27

Internal problem ID [6900]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 27
Date solved : Monday, January 27, 2025 at 02:34:27 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} x y^{\prime }-3 y x&=1 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

dsolve(x*diff(y(x),x)-3*x*y(x)=1,y(x), singsol=all)
 

\[ y = \left (-\operatorname {Ei}_{1}\left (3 x \right )+c_{1} \right ) {\mathrm e}^{3 x} \]

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 18

DSolve[x*D[y[x],x]-3*x*y[x]==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{3 x} (\operatorname {ExpIntegralEi}(-3 x)+c_1) \]