8.4.11 problem 11

Internal problem ID [714]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 11
Date solved : Tuesday, March 04, 2025 at 11:33:50 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 5

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

\[ y(x)\to 0 \]

✓ Sympy. Time used: 0.244 (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)
 

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