7.4.9 problem 9

Internal problem ID [81]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 9
Date solved : Friday, February 07, 2025 at 07:48:41 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=7 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 10

dsolve([x*diff(y(x),x)-y(x)=x,y(1) = 7],y(x), singsol=all)
 

\[ y = x \left (\ln \left (x \right )+7\right ) \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 11

DSolve[{x*D[y[x],x]-y[x]==x,{y[1]==7}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x (\log (x)+7) \]