2.4.9 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 : Tuesday, September 30, 2025 at 04:06:49 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*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 10

ode:=-y(x)+x*diff(y(x),x) = x; 
ic:=[y(1) = 7]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 11

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

\begin{align*} y(x)&\to x (\log (x)+7) \end{align*}

✓ Sympy. Time used: 0.093 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - x - y(x),0) 
ics = {y(1): 7} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x \left (\log {\left (x \right )} + 7\right ) \]