44.5.15 problem 4(e)

Internal problem ID [9171]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page 28
Problem number : 4(e)
Date solved : Tuesday, September 30, 2025 at 06:11:49 PM
CAS classification : [_linear]

\begin{align*} 2 x +3 y-1-4 \left (x +1\right ) y^{\prime }&=0 \end{align*}

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

ode:=2*x+3*y(x)-1-4*(1+x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x +1\right )^{{3}/{4}} c_1 +2 x +3 \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 20

ode=(2*x+3*y[x]-1)-4*(x+1)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 x+c_1 (x+1)^{3/4}+3 \end{align*}

✓ Sympy. Time used: 0.923 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x - (4*x + 4)*Derivative(y(x), x) + 3*y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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