Internal problem ID [62]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.5. Linear first order equations. Page 56
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {-y+y^{\prime } x -x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 7] \end {align*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 10
dsolve([-y(x)+x*diff(y(x),x) = x,y(1) = 7],y(x), singsol=all)
\[ y \relax (x ) = \left (\ln \relax (x )+7\right ) x \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 11
DSolve[{-y[x]+x*y'[x]== x,y[1]==7},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (\log (x)+7) \\ \end{align*}