44.3.11 problem 19

Internal problem ID [6992]
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. Review problems at page 34
Problem number : 19
Date solved : Monday, January 27, 2025 at 02:40:08 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+y&=2 x \end{align*}

With initial conditions

\begin{align*} y \left (x_{0} \right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 18

dsolve([x*diff(y(x),x)+y(x)=2*x,y(x__0) = 1],y(x), singsol=all)
 

\[ y = \frac {x^{2}-x_{0}^{2}+x_{0}}{x} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 19

DSolve[{x*D[y[x],x]+y[x]==2*x,{y[x0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^2-\text {x0}^2+\text {x0}}{x} \]