7.4.23 problem 23

Internal problem ID [95]
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 : 23
Date solved : Saturday, March 29, 2025 at 04:31:10 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+\left (2 x -3\right ) y&=4 x^{4} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=x*diff(y(x),x)+(2*x-3)*y(x) = 4*x^4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{3} \left ({\mathrm e}^{-2 x} c_1 +2\right ) \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 19

ode=x*D[y[x],x]+(2*x-3)*y[x]==4*x^4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^3 \left (2+c_1 e^{-2 x}\right ) \]

✓ Sympy. Time used: 0.320 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x**4 + x*Derivative(y(x), x) + (2*x - 3)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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