8.4.8 problem 8

Internal problem ID [711]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 8
Date solved : Tuesday, March 04, 2025 at 11:33:42 AM
CAS classification : [_linear]

\begin{align*} y+3 x y^{\prime }&=12 x \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

ode:=y(x)+3*x*diff(y(x),x) = 12*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 3 x +\frac {c_1}{x^{{1}/{3}}} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 17

ode=y[x]+3*x*D[y[x],x] == 12*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 3 x+\frac {c_1}{\sqrt [3]{x}} \]

✓ Sympy. Time used: 0.176 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x*Derivative(y(x), x) - 12*x + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{\sqrt [3]{x}} + 3 x \]