7.4.11 problem 11

Internal problem ID [83]
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 : 11
Date solved : Saturday, March 29, 2025 at 04:30:36 PM
CAS classification : [_separable]

\begin{align*} x y^{\prime }+y&=3 x y \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.017 (sec). Leaf size: 5

ode:=x*diff(y(x),x)+y(x) = 3*x*y(x); 
ic:=y(1) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 6

ode=x*D[y[x],x]+y[x]==3*x*y[x]; 
ic={y[1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 0 \]

✓ Sympy. Time used: 0.249 (sec). Leaf size: 3

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x*y(x) + x*Derivative(y(x), x) + y(x),0) 
ics = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 0 \]