8.4.10 problem 10

Internal problem ID [713]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 10
Date solved : Tuesday, March 04, 2025 at 11:33:48 AM
CAS classification : [_linear]

\begin{align*} -3 y+2 x y^{\prime }&=9 x^{3} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=-3*y(x)+2*x*diff(y(x),x) = 9*x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 3 x^{3}+x^{{3}/{2}} c_1 \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 19

ode=-3*y[x]+2*x*D[y[x],x] == 9*x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 3 x^3+c_1 x^{3/2} \]

✓ Sympy. Time used: 0.281 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-9*x**3 + 2*x*Derivative(y(x), x) - 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x^{\frac {3}{2}} + 3 x^{3} \]