7.3.4 problem 4

Internal problem ID [44]
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 1.4 (separable equations). Problems at page 43
Problem number : 4
Date solved : Tuesday, March 04, 2025 at 10:40:03 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 18

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

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

✓ Sympy. Time used: 0.260 (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)
 

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