8.4.23 problem 23

Internal problem ID [726]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 23
Date solved : Saturday, March 29, 2025 at 10:16:03 PM
CAS classification : [_linear]

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

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

ode:=(-3+2*x)*y(x)+x*diff(y(x),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: 0.031 (sec). Leaf size: 19

ode=(-3+2*x)*y[x]+x*D[y[x],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: 0.296 (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)
 

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