2.3.4 problem 4

Internal problem ID [680]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.4. Separable equations. Page 43
Problem number : 4
Date solved : Tuesday, September 30, 2025 at 04:05:43 AM
CAS classification : [_separable]

\begin{align*} \left (1+x \right ) y^{\prime }&=4 y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

ode:=(1+x)*diff(y(x),x) = 4*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \left (1+x \right )^{4} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 18

ode=(1+x)*D[y[x],x] == 4*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 (x+1)^4\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.199 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 1)*Derivative(y(x), x) - 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \left (x^{4} + 4 x^{3} + 6 x^{2} + 4 x + 1\right ) \]