8.4.9 problem 9

Internal problem ID [712]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 9
Date solved : Monday, January 27, 2025 at 02:58:57 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 10

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

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 11

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

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