7.4.10 problem 10

Internal problem ID [82]
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 : 10
Date solved : Saturday, March 29, 2025 at 04:30:34 PM
CAS classification : [_linear]

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

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

ode:=2*x*diff(y(x),x)-3*y(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=2*x*D[y[x],x]-3*y[x]==9*x^3; 
DSolve[ode,y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.274 (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)
 

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