8.6.5 problem 5

Internal problem ID [775]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 5
Date solved : Tuesday, March 04, 2025 at 11:44:42 AM
CAS classification : [_separable]

\begin{align*} 3 y+x^{4} y^{\prime }&=2 x y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

\[ y = c_1 \,{\mathrm e}^{\frac {1-x}{x^{3}}} \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 24

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

\begin{align*} y(x)\to c_1 e^{\frac {1-x}{x^3}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.526 (sec). Leaf size: 14

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

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